Black holes that occur in nature are most likely to be rotating coal black holes. If you try to travel in a straight line towards the center of such a rotating black hole, the frame dragging effect will instead cause your path to spiral in towards the black hole like a boat caught in the current of a whirlpool.
With that being said, it would be possible to cross the event horizon of supermassive black holes safely.
These are the black holes found at the centers of galaxies which have massive accretion disks and energetic jets. It is nearly impossible to represent the view near of this a black hole with a 100 per cent scientific accuracy.
In interstellar for example, the Doppler shifted light from the accretion disk was reduced to avoid confusing the audience. However, there are some simulations that are much more accurate scientifically speaking.
This simulation shows the approach to a realistic black hole with an accretion disk and jets. The set of circles at the bottom left are a map showing us where we are in relation to the black hole. The green represents the region outside of the innermost stable circular orbit. The yellow region is the area outside of the photon sphere where photons can orbit the black hole. The outer and inner red circles are the outer and inner event horizons. The clock at the bottom right shows the time on a clock falling in as read by an observer far from the black hole.
As we approach the black hole, we see the two orange color jets streaming outwards horizontally and the rotating accretion disk. As a result, all the dust and gas orbiting the black hole, it is difficult to see the location of the event horizon.
As we fall closer to the inner most stable circular orbit, our friends far from the black hole see our clock appears to tick very slowly.
Play video starting at 2 minutes 10 seconds and follow transcript2:10
As we cross through the event horizon, we continue to see the glowing gas outside of the black-hole. Light from all the stars and galaxies in the universe enters the black hole and is concentrated at the inner horizon leading to a blinding flash of light at the incident we smash into the singularity.
Play video starting at 2 minutes 32 seconds and follow transcript2:32
A trip into a supermassive black hole would take about four hours, but when observer faraway our trip across the event horizon appears to take an infinite amount of time. They would watch our clocks slow down the closer we approach the horizon, and would quickly get bored.
University of Alberta scientist, Eric Poisson and Werner Israel were the first physicists to show that the inner or Kushi horizon of a black hole is not traversable. For my own PhD work, I demonstrated that for any realistic black hole, once you enter the black holes event horizon, you cannot avoid hitting the singularity.
Play video starting at 3 minutes 13 seconds and follow transcript3:13
So, if you are interested in traveling to distant parts of the universe, entering a black hole is not a good idea. The singularity at the core of a black hole is an unavoidable obstacle. So, is it possible for space-time to warp in such a way that does permit long distance travel in the universe? In theory, yes.
Wormholes are hypothetical space-time structures that could act as bridges to different parts of the universe, but wormholes come with their own set of problems and challenges, and aren't much more likely to help you travel throughout the universe.
I grew up in the orchards of the Okanagan Valley in Canada and apples have been an important part of my life. Apples also played an important role in the work of Newton, as he reputedly described the moment he began to wonder about gravity as being the result of seeing an apple fall out of a tree. Often, an apple is used as an analogy to describe another important concept in gravitational physics.
I'm talking about a specific solution to Einstein's field equations, the Schwarzschild wormhole. Of course, the name wormhole comes from the idea that worms or caterpillars who feast on the flesh of an apple can tunnel through the interior in order to create a shorter path between two points on the surface.
In this analogy, the skin of the apple is our regular four-dimensional spacetime and the flesh of the apple of some higher dimension in a hyperspace. Carl Sagan famously said about wormholes, "It's just possible that you might emerge in another part of spacetime, some where else in space, some when else in time."
So what exactly is a wormhole? The short answer is that a wormhole looks like a black hole. But instead of a trash compacting singularity at the center, a wormhole opens back up into a distant region of spacetime.
In 1916, Ludwig Flamm was studying the Schwarzschild black hole solution to Einstein's field equations, when he discovered that a second solution was possible. This second solution described a white hole, a region in space that ejects matter from its event horizon.
Flamm then lined up and joined the necks of both the black hole and the white hole and boom, the concept of a spacetime bridge was born. Today, we call this an Einstein-Rosen bridge after it was rediscovered by Einstein and Rosen in 1935.
It wasn't until 1957 that the word wormhole was first used to describe a connection between two points in spacetime. This time by scientist Charles Misner and John Wheeler.
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Let's be very clear right off the bat here, white holes and wormholes are purely hypothetical and unlike black holes, there's no observational evidence of their existence. Mathematically speaking, wormholes can exist and not only can they tunnel through space but it's also possible for them to tunnel through time.
Throughout the 60's, 70's and 80's, wormholes entered popular culture through novels like A Wrinkle In Time, The Forever War, and Carl Sagan's Contact. Even modern video games like Portal and Portal 2 employ wormholes as their central game mechanic. In fact, the mathematical development of wormhole theories seems to be heavily influenced by science fiction.
When Carl Sagan was writing his science fiction novel, Contact, he approached the famous black hole physicist, Kip Thorne, and asked him how it will be possible for a human being to travel vast distances across the galaxy using a rotating black hole. Thorne suggested instead that Carl consider travelling through wormholes. When Thorne put pen to paper to start figuring out the mathematics, they discovered that wormholes are inherently unstable.
Not only would the neck of a Schwarzschild wormhole be too narrow to permit the passage of human being, but the wormhole itself would close up extremely quickly making it possible to only squeeze through a bit of information before the wormhole is destroyed.
However, Thorne realized the neck of the wormhole could be held open with some kind of material that would repel the wormhole's walls gravitationally. In reality, we have no idea what kind of material this would be, all of the regular material in our universe acts through gravitational attraction. If regular matter won't do the job, Thorne posited that a spherical wormhole could be kept open using a form of material with a negative energy density.
In fact, when the University of Alberta's physicist Don Page was approached by Thorne, Page demonstrated that any shape of wormhole requires a negative energy density to be held open in much more elegant mathematics. Physicists call this exotic material and although there are no examples that we know of, there's nothing written in the laws of physics that prevent it from existing in our universe. The distinguishing feature between an unstable and a traversable wormhole is therefore, the presence of this exotic material.
One such traversable wormhole was theorized by a scientist named Homer Ellis, who demonstrated a solution to the Einstein field equations that permit safe passage through the wormhole in either direction. Named after him, the Ellis wormhole was used as a template for the wormhole in Interstellar, which carries the crew of the Endurance from orbit around Saturn to Gargantua in a distant region of the universe.
We don't touch much on the science of time travel but one of my favorite movies on the subject has to be Back to the Future. In it, Doc Brown accidentally sends Marty McFly travelling backwards in time from the year 1985 to 1955 in his time travelling DeLorean. One of my favorite fan theories for how the DeLorean works, is that the flux capacitor stores enough energy, 1.21 giga-watts, and not jiga as Doc Brown says, to create the negative energy density required to amplify a tiny wormhole. Just big enough and just long enough for the DeLorean and its passengers to squeeze through the wormhole before it closes behind them.
06.04 -회전하는 블랙홀(Spinning Black Holes) [커세라 강의 페이지]
There have only been a few occasions where we have discussed the properties of a rotating black hole. Back in module five for example, we discovered that the rotation of a black hole changes the location of the innermost stable circular orbit. For a non-rotating black hole, the ISCO was three times farther from the center of the black hole than its Schwarzschild event horizon. But for a rotating black hole, the ISCO can shrink until it exactly matches up with the black holes event horizon. It should be noted that as a black hole spins faster and faster, it also pulls the event horizon inwards. Both the ISCO and the event horizon can be as small as half of a Schwarzschild radius for a maximally rotating black hole.
In fact, now would be a good time for us to fess up about a little white lie we've been telling you. Any realistic black hole will have angular momentum and will therefore be spinning. We know that black holes must be spinning because in-falling particles carry angular momentum, and we have a pesky law of conservation of angular momentum, which tells us that particles will contribute angular momentum to the black hole. While it's convenient for scientists to learn about the properties of black holes from non-rotating solutions, the reality is that the perfect Schwarzschild black hole is unlikely to exist.
We should also note something very strange about black hole rotation. There is a limit to how quickly they can spin. We'll talk a little bit more about the mathematics behind this concept shortly, but the basic idea is that the rotation of a black hole drags spacetime along with it. Similar to the way that water spirals down a drain, spacetime rotates around a rotating black hole. This is a process called frame-dragging.
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01:45
The rotation of a black hole depends on its original spin and the cumulative effects brought about by all of the material that has fallen into it. A problem arises when we begin to talk about angular momentum. Previously, we had taken an object's mass and multiplied it by the distance from the point of rotation to calculate its moment of inertia.
Do you see the problem here? If all the mass of a black hole is trapped within a zero volume singularity at its center, how is it possible for a black hole to have a moment of inertia?
Well, in 1963, a scientist named Roy Kerr developed a solution to Einstein's field equations which precisely described the properties of a rotating black hole. In the original research, Kerr described how he characterized the angular momentum of a black hole, but mentions how the moment of inertia cannot be characterized except to say that they are very small.
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The rotation of black holes is usually characterized by a number between zero and one called a, which is calculated by the equation, a equals J times c divided by M squared G. J is the angular momentum of the black hole, M is its mass, and G is Newton's gravitational constant. If you haven't figured it out already, lowercase c is always used to describe the speed of light. If a black hole is not rotating at all, unlikely I know, a takes on the value of zero. If a black hole is spinning maximally, meaning it has reached the upper limit we mentioned before, a takes on a value of one. As the black hole spins faster, the event horizon and the ISCO are pulled inwards. The rotating black holes event horizon shrinks to about half the size of a non-rotating Schwarzschild black hole with the same mass, and the ISCO decreases from three times the Schwarzschild radius to coincide with the event horizon at half the Schwarzschild radius from maximum rotation.
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With that said, I now feel comfortable showing you how the radius of the ISCO changes from three times the Schwarzschild radius down to one-half as rotation of the black hole changes from a equals zero to a equals one.
In case you're wondering, the maximum allowed spin frequency at the event horizon of a solar mass black hole is 16,000 Hertz. The event horizon of a black hole with the same mass as the sun can spin as fast as 16,000 times per second. For other masses, we can simply calculate the maximum spin rate as 16,000 Hertz times the mass of the sun divided by the mass of a black hole.
Therefore, higher mass black holes must spin at a slower rate. For a black hole about 36 times the mass of the sun, you would find the maximum rotation corresponds with about 440 Hertz or for you music aficionados, the same as a concert 'a' note.
The underlying mathematics of Kerr solution would take an entire course to discuss, but its impact within the scientific community is characterized best by Nobel Prize winning physicist, Chandrasekhar who said,
"In my entire scientific life extending over 45 years, the most shattering experience has been the realization that an exact solution of Einstein's equations of general relativity discovered by New Zealand mathematician, Roy Kerr provide an absolute exact representation of the untold number of massive black holes that populate the universe".
Play video starting at 5 minutes 17 seconds and follow transcript5:17
As a rotating black hole twist the spacetime around it like the ripples in a whirlpool, the twisting and warping of spacetime itself begins influencing the particles and objects within it. Far from the black hole, these forces gently swirl objects around the black hole. The closer you approach the event horizon of a rotating black hole, the more extreme this interaction becomes eventually pulling anything falling past the event horizon into complete lockstep with the black hole.
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Let's have a top-down look at a non-rotating Schwarzschild black hole. In this diagram, there is a central non-rotating black hole and each point here represents some source of light. When a light source is far from the black hole, the light propagates outwards in all directions. As the sources approach the event horizon, the light sphere begins to distort towards the black hole center.
When one of these light sources crosses the event horizon, the light becomes trapped inside.
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Now, let's impart some spin on this black hole changing it from a Schwarzschild black hole into a rotating Kerr black hole. Since the Kerr black hole just drag spacetime, light sources far from the black hole begin to see a shift in the direction their light spheres propagate. But there's an even more interesting change when a black hole is rotating. Not only does the event horizon shrink from the non-rotating Schwarzschild radius down to about half of its normal size for maximum rotation, but particles falling directly inward begin spiraling around the black hole even though there are no forces acting on them.
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There's a special distance from a rotating black hole that defines a region called the ergosphere. The outer boundary of the ergosphere is called the stationary limit and outside of the stationary limit, a spacecraft can park with respect to the black hole.
But within the stationary limit, no spacecraft can ever appear at rest to a distant observer. Even spacecraft entering the ergosphere orbiting the opposite direction to the rotation of the black hole will eventually be pulled by the spiraling spacetime into a co-rotating trajectory.
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Although the word sphere is part of ergosphere, the ergosphere is not actually spherical but rather an ellipsoid. While the event horizon is still spherical, the ergosphere envelops the event horizon only touching at the spin axis of the event horizon. It's good to remind ourselves that the ergosphere and the event horizon are boundaries and not objects, so they don't interact with each other in the same way that particles interact with them.
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0749
I'll emphasize now that a clever spaceship captain can still escape from the ergosphere, and can in fact steal rotational energy from the black hole. The word ergosphere comes from the Greek root ergon, which means work. The ergosphere is so-named because it's theoretically possible to extract the energy from the black hole's rotation with some clever tricks.
For example, from within the ergosphere, you could throw a ship's garbage against the rotation of the black hole, accelerating the ship forward and in the spiraled spacetime, end up with more kinetic energy than you started out with. In a case like this, you're stealing energy from a black hole's rotation. Roger Penrose first described this process of stealing energy from a rotating black hole in 1971, which is why we call it the Penrose process.
Without going into detail, within the ergosphere, it's possible for the energy of a particle to become negative, a consequence of the change in coordinate system at the stationary limit. Ultimately, what this means is a super-advanced civilization could survive around a rotating black hole, extracting a surplus of energy using the Penrose process until a black hole's rotational energy has been sapped.
They could also do the reverse, storing energy as the angular momentum of a black hole and extracting it at a later time.
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0910
It might seem far-fetched to you to be talking about spiralling spacetime and frame dragging, but it's possible to measure the gravitational effects of a rotating body without a black hole at all.
In fact, a space probe aptly called Gravity Probe B was launched back in 2004 to investigate just how strong the frame dragging effects are here on earth. Gravity Probe B carried four incredibly precise gyroscopes in order to measure these effects. At the time of their construction, these gyroscopes were the most spherical objects ever made, differing from perfectly round by no more than 40 atoms on a sphere roughly the size of a ping pong ball.
Since the effects are quite a bit weaker around a planet like Earth compared to black holes, it took four years of operation before NASA reported agreement with Einstein's theory of general relativity.
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1006
We've been hiding a few details of the Kerr black hole behind the veil as it were. The event horizon of a Kerr black hole should really be called its outer horizon because the mathematics tell us that there must be another inner horizon hidden inside. The outer horizon is basically the same as the event horizon; it's the boundary from which nothing can escape. Even if you've fallen through the outer horizon, it's still possible to receive information from beyond the event horizon right up until you fall through the inner horizon often called the Cauchy horizon.
The Cauchy horizon marks the boundary within a black hole where information from the entire history of the universe is compressed. An observer approaching the Cauchy horizon would see more and more of the history of the universe essentially being battered by the extreme energies that are compressed within that region. Crossing the Cauchy horizon would be perilous enough simply due to the incredible energy densities one would need to survive. But there's yet another mathematical danger lurking within the Cauchy horizon, the Kerr black hole's ring singularity.
Unlike the point-like singularities we've been discussing for Schwarzschild black holes, the singularity of a rotating Kerr black hole is a ring instead of a point. The Cauchy horizon may be the universe's last stand at preventing observers from violating cosmic censorship and glimpsing the singularity.
What happens if the black hole spin increases? The distance between the outer and inner horizons become smaller, and the two horizons will coincide if the black hole has maximal rotation. If the black hole spins faster than maximal rotation, the equations predict that the horizons will disappear and the singularity will become visible to the whole universe.
Since there will be no event horizon, the resulting thing will not be a black hole, instead we call it a naked singularity.
Cosmic censorship predicts that it is impossible to spin a black hole faster than the maximal amount.
One final note about rotating black holes. If it were possible to pass through the Cauchy horizon and if it were possible to survive the cosmic censor, it might be possible that an extremely talented astronaut could pilot their ship past the ring singularity and emerge into another universe.
What that universe might look like or what you would find there is still unknown. While it may be tempting to plunge into a Kerr black hole hoping to survive the journey to a new universe, there may be a less dangerous possibility which we'll talk about next: worm holes.
How can you determine if a black hole is spinning?
블랙홀이 회전하는지 어떻게 알까?
Interview with Dr. Fiona Harrison, Professor at Caltech University
NuStar is able to tell whether black holes are spinning or not.
우주 X-선 망원경 누스타 NuStar 는 우리에게 블랙홀이 회전하는지 아닌지 알수있는 관측자료를 보내줄 겁니니다.
Black holes astrophysically are pretty simple, they only have two parameters, mass and spin. And when matter falls onto a black hole, attracted by its gravity, it organizes itself into what's called an accretion disk.
블랙홀을 천체물리의 관점에서 보면 아주단순합니다. 그저 두개의 인자, 질량과 회전으로 특징지을 수 있죠. 중력으로 인해 끌려 들어간 물질들은 강착 원반을 형성합니다.
And friction in this disk heats the material up so that when you get very close to the black hole, if it's super massive black hole, it's emitting in the optical or ultraviolet. And then you have regions where particles get accelerated very close to the speed of light, and these emit high energy X-rays.
거대한 규모의 강착원반에서 안쪽 원과 바깥쪽원의 회전 속도차로 인한 마찰은 물질들을 가열시킵니다. 블랙홀에 가까운 안쪽 원반일수록 온도가 높다. 거대 질량 블랙홀의 경우 가시광에서 자외선 범위까지 빛을 낸다[열복사]. (강착 원반내) 입자들이 거의 빛의 속도까지가 속되면 고에너지 X-선을 방출합니다.
These high energy X-rays can act like a light bulb, shining down on this accretion disk and reflecting X-ray light off of it. Now, by then analyzing that reflected X-ray light, we can tell the geometry of the accretion disk, and in particular, most importantly, how close does it come to the black hole.
이 고에너지 X선은 마치 전구 같이 작동하여 강착원반을 비추고 강착 원반에서 반사된 빛이 나오죠. 반사된 X선을 관찰 함으로서 강착 원반의 기하학적인 모습을 알수 있습니다. 특히 중요하게 보는 점은 강착 원반이 블랙홀에 얼마나 가깝게 있냐는 것입니다.
If the black hole is not spinning, the closest it can come is six gravitational radii, all right? Don't worry too much if you don't know what a gravitational radius is, it's six, okay? If the black hole is spinning maximally, then the accretion disk can come down to one gravitational radius. And we can tell this by analyzing that reflected X-ray spectrum off of the accretion disk. And therefore tell how rapidly the black hole is spinning.
만일 블랙홀이 회전하지 않는다면 가장 근접한 원반 띠는 6중력 반경이 될 것이다. 중력 반경이라는 말을 처음 듣는다면 걱정하지 말고 그냥 6이라고 하죠. 만일 블랙홀이 최대 속도로 회전한다면 강착 원반의 최내곽 띠의 중력반경은 1로 (이론 상) 떨어집니다. 강착 원반이 반사한 X선을 분석하면 맞는지 알수 있습니다. 그로부터 블랙홀이 회전하는 속도도 알아낼 수 있죠.
Now, let's do something unwise, and travel past the event horizon of a black hole. Knowing that we'd like to get there without being spaghettified, let's choose a supermassive black hole as our destination so that tidal forces don't rip us apart on our approach.
약간 현명치 못한짓을 해보자. 블랙홀의 사건 지평선을 통과해 보는 것이다. 늘어진 스파게티가 되는 걸 피하려면 초거대 규모 블랙홀을 골라야지 안 그러면 산산조각 날거다.
Once we pass through the event horizon, we will be in the strange world of a black hole's interior. Although it is impossible to send information about the inside of the black hole to the universe beyond the event horizon, there are no laws of physics that would prevent us, observers within the event horizon from making scientific discoveries.
사건의 지평선을 스치면서 블랙홀 내부를 엿볼 수 있으면 좋겠다. 블랙홀 내부에서 외부 우주로정보를 내보낼 수는 없지만 어느 물리법칙으로 우리의 호기심을 막을 수 있겠는가. 사건의 지평선안에 들어가 어떤 과학적 원리를 찾을 수 있을지 궁금하다.
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The first thing that we would notice looking away from the black hole is all of the light emitted by the stars and galaxies outside of the black hole. It definitely isn't black inside a black hole. If we shine a flashlight, we find that no matter what direction we try to aim the light, the rays always end up pointing inward to smaller values of the black hole's radius.
먼저, 블랙홀에서 밖을 내다보면 은하와 별들이 빛을 내고 있는 모습을 볼 수 있다. 블랙홀 안에 있다고 암흑 천지라는 의미는 아니다. 손전등을 비추면 방향이 어떻든 빛 줄기는 항상 블랙홀의 중심을 향할 뿐이다.
Before we examine the peculiarities inside of the event horizon, it's worth pointing out just how strange our universe actually is. We have three spatial dimensions that allow us to move about front to back, left and right, as well as up and down.
사건지평선 내부의 이상한 모습을 살피기 전에 우리가 살고 있는 우주부터 보자. 우리는 삼차원공간에 있다. 상하좌우 그리고 앞뒤 이렇게 세개축으로 움직일 수 있다.
We also consider time, a dimension even though we can only move forward. Something very peculiar happens to the dimensions of space and time at the event horizon of a black hole. Within the event horizon, the radial coordinate, which measures how far you are from the black hole singularity, switches meaning with the dimension of time.
시간을 생각해 보자. 우리의 시간은 앞으로 흐르기만 한다. 그런데 블랙홀의 사건지평선을 넘으면 시공간의 차원이 이상해 진다. 사건 지평선 안에서는 방사형 좌표계(radial coordinate)가 시간과 함께 의미있을 뿐이다. 방사형 좌표계는 블랙홀의 중심인 특이점에서 떨어진 거리를 시간의 차원으로 변환하여 의미를 둔다.
* 여기 언급된 radial coordinate는 polar coordinate system을 의미하지 않는다.
Think about it like this, when we're out and about in the universe, we cannot go backwards in time. But in the interior of a black hole, we can no longer go backwards in space. This may give you a headache, but moving to smaller values of radius is really the same thing as moving towards a time in the future.
이렇게 생각해 보자. 우리가 우주에 있으면 시간을 뒤로 돌릴 수 없다. 그럼 블랙홀 안에 있다면 공간을 뒤로 돌릴 수 없다. 좀 헛갈릴텐데, 반경을 조금 줄이면 미래로 시간이 갔다는 의미가 된다.
Escaping the black hole would require that you move to larger values of radius, which is equivalent to going backwards in time. Since you can't go backwards in time, you have no choice but to continue to future times, which is the same thing as moving towards smaller value of radius towards the center of the black hole.
블랙홀에서 탈출은 반경을 크게 늘렸다는 것이고 시간을 한참 과거로 돌린 것과 같다. 시간은 오직 미래로 간다는 뜻은 블랙홀 중심을 향한 반경이 항상 줄어든다는 의미와 같게 된다.
This might not make much sense if you are thinking of the black hole as a sphere surrounding the point r equals zero. This is a good enough picture for the region outside of the event horizon, but it is not a good representation of the inside of a black hole.
쉽게 와닿지 않겠지만 블랙홀을 반지름 r이 0인 구(sphere)라고 해보자. 아래 그림을 보자. 사건 지평선의 외부를 보여주기에 충분한 그림이긴 한데 블랙홀 내부를 전혀 보여주지 못한다.
We can make a better picture of a black hole by first thinking about how to represent a star that has the same size for all time.
영원히 크기가 변하지 않는 별을 표현하는 방법을 먼저 궁리해 보고 나서 블랙홀을 어덯게 그림으로 표현할지 생각해보자.
In this diagram, since the star is a sphere, all we show is the size of the star's radius. Time runs upwards in this diagram and to the right, we plot distance from the center of the star. Since the star has the same size for all time, the surface of the star is just a straight vertical line.
이 그림에서 별은 구 이므로 별의 반경이 항상 같으므로 구면도 변함이 없다. 그림에서 수직선은 시간 축이고 수평축은 별의 중심에서 반경을 나타낸다. 별의 크기가 항상 같으므로 별의 표면은 반지름에서 수직인 선이다.
[아주 단순하게 표현한 시간과 공간을 결합한 시공간 도표다. 공간을 한개의 축으로 단순화 했다. 시간을 포함한 4개의 차원을 도식화 하기 어려워서 그렇지 우리는 시간이 흐르면서 공간이 변하는 시공간에서 살고 있다. 공간 속에서 위치를 인위적으로 바꿀 수 있지만 시간을 앞뒤로 움직일 수 없다는 한계가 있긴하다. 그런데 어떤 존재가 공간을 휘어 놓는다면 우리가 제어 할 수 있다던 공간상의 위치도 우리 것이 아닐 수도 있다.]
On this diagram, light rays travel on 45-degree angle lines.
이 도표에서 빛은 45도 각도의 직선이다. [빛의 속도는 항상 같다.]
Now, let's draw a picture of a star that is a sphere that is collapsing to become smaller in size. We are using the same coordinates on this graph, so the surface of the star is a curve instead of a straight line. As time increases upwards on this graph, the distance between the surface of the star and the center of the star decreases with time.
이번에는 구의 크기가 쪼그라 드는 붕괴하는 별을 그려보자. 앞서 그림에서 본 그래프와 동일한 좌표계다. 시간이 갈수록 반지름이 줄어드는 별의 표면은 수직선 대신 곡선을 그린다. 윗쪽으로 시간이 흐를수록 반지름이 줄어든다.
Now, let's take the collapsing star and allow it to form a black hole. In this picture, we have the same surface of the star; they get smaller as time increases. But at one special moment in time, the surface of the star is at the same location as the Schwarzschild radius, Rs.
별이 붕괴하면서 블랙홀이 되는 과정을 그려보자. 그림에서 어떤 별이 시간이 흐르며 작아지고 있다. [이별의 질량에 큰 변화가 없다고 치면] 줄어드는 표면과 슈발츠쉴트 반경 Rs 이 만나는 점이 있다.
[Rs는 단지 질량에 비례한다. 별이 붕괴 하더라도 질량은 변함 없다고 하자]
At this moment of time, the event horizon forms and is represented by a straight line drawn at a 45-degree angle.
이 점에서 사건의 지평선이 생기고 45도 직선이 사건의 지평선을 나타낸다.
The region below the event horizon is the region outside of the black hole, and the region above the event horizon is the inside of the black hole.
사건의 지평선의 아랫 영역을 블랙홀의 외부라 하고 윗 영역을 블랙홀 내부라 하자.
The jagged line corresponding to what we thought was a point is actually a time in the future. This is a simplified version of a Penrose diagram, which is a tool scientists use to understand the interiors of black holes.
물결친 수평선은 우리가 주목하는 것인데 앞으로 다뤄야할 특이점이다. 이 도표를 펜로스 도(Penrose diagram)라고 한다. 블랙홀의 안쪽을 이해할 때 과학자들이 동원하는 도표다.
More advanced versions of Penrose diagrams further compactify the dimensions of space to a finite region. Since the radial coordinate r takes on the characteristic of a time coordinate, smaller values of distance from the center correspond to later times. There is no way to avoid the flow of time, so any object that is dropped into the event horizon ends up falling to the center at r equals zero.
좀더 고난도 펜로스 도는 공간의 차원을 무한한 영역으로 확장한 것이다. 방사좌표계의 거리 r 은 시간 축에 의존 하므로 중심으로부터 거리의 작은 값은 미래 시간에 대응한다. [반경의 변화가 곧 시간의 흐름을 의미한다. 공간이 곧 시간이다.] 시간을 거스를 방법은 없다. 따라서 사건의 지평선에 들어온 어떤 물체도 반경 r 이 0인 중심으로 떨어진다.
In this diagram, light rays travel on upward paths at 45 degrees. Light emitted in the region outside of the event horizon can go in two directions, the right, which means escaping from the black hole; or to the left, which means falling into the event horizon.
이 도표에서 빛은 위쪽 45도 방향으로 향하고 있다. 사건 지평선 바깥 영역에서 방출된 빛줄기의 경로는 두 방향을 취한다. 오른쪽은 블랙홀에 붙들리지 않았다는 의미이며, 왼쪽은 블랙홀로 빨려 들어 간다는 뜻이다.
Light that is emitted inside of the event horizon still travels on upward directed 45-degree angled lines. Light that is sent in either left or right hits the jagged r equals zero line.
사건의 지평선 안에서 방출되는 빛도 좌우 45도 위로 나간다. 좌측 상단으로 나가든 우측 상단으로 나가든 결국 r 이 0인 물결선에 닿는다.
Having a powerful rocket engine won't help you escape. All this can do is slow down the inevitable since your rocket can't travel faster than light. The amount of your own personal proper time that it takes to fall from the event horizon to the center of the black hole depends on the mass of the black hole.
로켓에 제아무리 강력한 엔진을 달았어도 빠져 나갈수 없다. 결국 천천히 주저 앉을 텐데 빛보다 빨리 움직일 수 없기 때문이다. 사건의 지평선에서 블랙홀까지 떨어지는 동안 주어진 시간은 블랙홀의 질량에 달렸다. [떨어지는 물체의 무게와는 상관 없다는 걸 이미 갈릴레오 시대부터 증명되었던 사실이다.]
A higher mass black hole is larger in size and the fall takes more time. The time it takes to reach the center is characterized by this tidy equation, time to fall equals 15 microseconds times the black hole mass divided by the sun's mass.
So for the black hole Cygnus X-1 with a mass that is 15 times larger than our sun's, the equation dictates that you'd have about 0.2 milliseconds to relish in the experience of touring the black hole's interior. This amount of time is about how quickly your eyelids take to blink, so you won't even be able to think about snapping a photo of the scene.
We now have another great reason to visit high mass black holes. We can have more time to enjoy the sights. For example, if we were to choose a supermassive black hole that is one billion times the mass of the sun, we'd have around four hours of proper time to fall from the event horizon to the singularity at the center.
질량이 큰 블랙홀 일 수록 관광을 즐길 시간을 더 많이 가질 수 있다. 태양질량의 10억배 쯤 되는 블랙홀의 경우 사건 지평선에서 중심의 특이점까지 떨어지는데 약 4시간정도 여유가 있다.
The center of the black hole at zero radius is location of the singularity. Since this location corresponds to a time in the future, you would not see or experience it until the precise moment of time when you reach it.
반경이 0인 블랙홀의 중심으 특이점이다.
How would objects behave when they arrive at the singularity? Well, since observers aren't able to report back what happens here, we examine what theoretical models of the interior tell us. No matter how massive the black hole, the equation suggest that all of the mass that has fallen into the black hole accumulates at the center and is squashed into zero volume. They also predict that an observer would feel infinitely strong gravitational and tidal forces from which no known object would survive destruction.
At this point, you might be a bit confused about the terminology, so let's unpack the word singularity a bit more.
물리학과 수학에서 말하는 특이점은 용어상 혼란이 있으니 이에 대해 먼저 풀어보고 가자.
To start, I'll state that physics and mathematics have an unequal relationship. In order for physicists to make predictions about physical processes, we need mathematical equations in order to describe likely outcomes.
However, it is possible to write down all sorts of mathematical expressions that don't seem to have any connection to physics at all.
Many times in the history of science, mathematicians have come up with equations that don't seem to have anything to do with physics. At only many years later, does some physicist discover that the equations actually describe some physical phenomenon.
과학의 역사상 수차례에 걸쳐 수학자들은 방정식을 만들어 왔는데 물리학과는 어울리지 않아 보였다. 방정식이 발표된 후 수년이 지난 후에야 몇몇 물리학자들이 그 방정식이 실은 물리 현상을 기술하는데 적합 하다는 것을 알아냈다.
Mathematical equations that describe physical processes are limited to certain circumstances. Outside of those limits, the equations begin to fail, giving non-physical answers. For an example, consider Newton's equation for the attractive gravitational force between two objects with mass one and two separated by a distance r.
Force equals G times mass one times mass two divided by the square of the radius. What happens if we allow the distance r between the two objects to come infinitely close together allowing the masses to occupy the same spot in space.
수식으로 표현된 물리현상이 수학적으로 받아들일 수 없는 경우의 예로 뉴튼의 만유인력 법칙이다.
In that case, we would set r in the equation to zero, which would mean that we would be dividing by zero in this equation. Dividing by zero is undefined in mathematics and is normally something that you should avoid doing.
두 물체 사이의 거리가 아주 가깝다면 만유인력은 0으로 나눠 힘은 무한대가 된다. 0으로 나누는 수식은 수학에서는 용서할 수 없다. [그래서 미분이 나오긴 했다.]
In order to make sense of this situation, we provide some physical context. What we should remember is that mass takes up space. So, it is physically impossible for the centers of two masses to have zero separation. Since Newton's equation of gravity fails when r equals zero, we should treat them only as a good description of nature if the distance between the objects is bigger than zero.
이 상황을 피하기 위해 물리학에서 마련한 방책은 질량을 가진 물체는 공간을 차지하므로 두 물채의 거리가 0이 될 수 없다는 조건을 붙여 놓았다. 두물체 사이에 거리가 0만 아니면 자연을 기술하는 훌륭한 수식이다.
The result when r equals zero is called a singularity. What this tells us is that at r equals zero, our equations just don't make any sense. This type of situation is one that prompts us as scientists to look for a new explanation and more specifically a new equation.
거리 r 이 0이되는 결과를 낳는 경우를 [수학적으로 존재할 수 없으니] 특이점이라고 한다. 이런 상황이 상정되면 우리는 과학자들에게 새로운 방정식을 내놓으라고 촉구한다.
We already learned that Newton's equation of gravity is an approximation to those of Einstein. Does that mean Einstein's description of gravity could help us remove the pesky singularity at the center of black holes? Unfortunately, the answer is no.
우리는 이미 뉴턴의 방정식이 아인슈타인의 중력관련 방정식을 근사화해서 얻을 수 있다는 것을 알고 있다. 아인슈타인이 중력에 관해 기술한 방정식이 블랙홀 중심의 성가신 특이점의 문제를 해소하는데 도움을 줄 수 있다는 뜻일까? 아쉽게도 답은 그렇지 못하다.
In fact, Einstein's equations predict a divergence of the gravitational fields. Meaning, the problem of the singularity gets even more troublesome than we would have otherwise predicted using Newton's equation.
사실 아인슈타인의 방정식은 중력장의 발산을 예측했을 뿐이다. [아인슈타인은 (미분) 방정식을 세웠지 해를 구하진 못했다. 지금도 여전히 다양한 해를 가져와서 해석을 내놓는 중이다.] 무슨 말이냐면 특이점의 문제가 (파면 팔수록) 뉴튼의 방정식 보다 더 만은 문제를 낳고 있다. [뉴튼의 만유인력 관계식은 거리만 해결하면 문제없다.]
One shortcoming of Einstein's equations for gravity is that they do not include our modern knowledge of quantum mechanics. Quantum mechanics distinguishes itself by introducing the concept of wave functions to describe the positions of particles. Quantum mechanics governs the behavior of particles at scales where Einstein's equations fail.
아인슈타인의 중력에 관한 방정식의 한가지 약점이라면 양자역학을 고려하지 않았다는 점이다. 양자역학은 파동함수를 도입하여 입자 스스로 위치를 결정한다. [위치의 문제다. 두 입자의 위치가 바로 거리다. 특이점 또한 거리(반경)의 문제다.] 양자역학은 아인슈타인이 놓친 입자 수준에서 그 행동을 지배(기술)한다.
Einstein's equations for gravity assumed that we know the locations and speeds of particles exactly. However, the Heisenberg uncertainty principle, a foundational concept of quantum mechanics, tells us that there is a limit to how precisely we can determine the location and speed of particles.
아인슈타인의 중력 방정식은 우리가 입자의 위치와 속도를 정확히 알고 있다고 가정한다. 하지만 양자역학의 기본 개념인 하이젠버그의 불확정성 원리는 우리가 입자의 위치와 속도를 정확히 한정하기는 제한이 있다고 말한다.
In order for physicists to understand the behavior of the singularity, we need to combine quantum theory with general relativity, which remains a mystery at present. If we knew how to create such a theory, we would call it quantum gravity.
물리학자들은 특이점의 행동(양태)을 이해하기 위해서 양자론과 상대론 엮어야 한다고 하지만 여전히 풀리지 않고 있다. 이런 이론을 만들어 낼 수 있다면 그것을 양자중력론 이라고 부르기로 하자.
One proposed method is called string theory and is a promising set of equations that might describe quantum gravity. However, scientists have not yet managed to solve these equations or make any useful predictions with them.
한 해법으로 끈 이론()이 떠오르고 있다. 복수의 가능성있는 방정식이 양자중력을 기술한다고 한다. 하지만 과학자들은 아직 해에 대한 해석을 내놓지 못하고 있고 그 방정식들이 어떤 결과를 내놓을이 유용한 예측도 못하고 있다. [개념만 있다.]
You dear listeners, can take this up as a challenge, the prize for successfully deriving a theory of quantum gravity could win you a Nobel Prize.
Many physicists think that as you fall in towards the black hole singularity, the standard equations of Einstein's gravity describe what happens to you for most of the trip, until the distance or really time between you and the singularity becomes much smaller than the size of an atomic nucleus. The region of spacetime that is close to the singularity requires quantum gravity for accurate predictions. Since we don't understand quantum gravity, we can only speculate. Perhaps, quantum gravity removes the concept of a singularity and could potentially describe the existence of a nice remnant.
많은 물리학자들은 아인슈타인의 중력이론의 표준 방정식이 블랙홀의 중심에 이르기 전까지, 그러니까 특이점 반경이 원자 핵 이하의 크기가 되는 영역까지는 잘 맞을 것이라고 생각한다. 특이점에 가까워 지면 시공간의 정확한 예측을 위해선 양자 중력이론이 요구될 것이다. 우리는 아직 양자중력을 확실히 이해하고 있지 못하기 때문에 추정만 할 뿐이다. 아마도 양자중력은 특이점의 개념을 타파하고 뭔가 새로운 설명을 남길 것이다.
We really have no way of knowing, since the singularity occurs at a time in the future and it can't affect us as we fall in. Ultimately, our lack of understanding of quantum gravity, doesn't affect our journey to the center of the black hole until the moment when we're about to reach the singularity.
As we have alluded to before, the singularity inside of a Schwarzschild black hole is a bit of a pesky mathematical object. The singularity simultaneously exists everywhere at the interior of a black hole but only at a specific moment of time. Given that singularities in our universe are not visible to us as far as we can tell they are all hidden behind event horizons, scientists have conjectured the existence of a principle to hide singularities from view, called the cosmic censorship hypothesis.
Einstein's gravitational equations predict many different types of singularities. We'll encounter a new type of black hole singularity shortly, a ring singularity. These other singularities are more like a wall that has a fixed location in space and last for a long time. Suppose you run towards the wall, you can see it in front of you as you approach it and if you don't stop, you'll smash into it. A singularity that is like a wall is called a naked singularity. A naked singularity is problematic since we don't have any way to protect what it might emit.
The cosmic censorship conjecture states that in realistic astrophysical situations, naked singularities can't form. In other words, the laws of physics keep singularities cloaked by event horizons. Possibly, only singularities like the Schwarzschild version can exist.
The cosmic censorship conjecture is yet unproven but at present, we do not see any evidence for naked singularities existing in nature. Well, with one exception, the Big Bang itself is quite possibly a naked singularity. It's likely that in nature, all singularities are surrounded by event horizons. Which is why I'm excited about direct observational evidence for the event horizon of a black hole.
Interview with Dr. Valeri Frolov, Professor at the University of Alberta
앨버타 대학의 교수 발레리 프롤로프 박사와 인터뷰
When you fall down to the center this squeezing and stretching forces increase infinitely. They destroy all the elements, all the very ones, all the elementary particles and when you come to the center physically, theoretically this forces grow to infinity. Physically, it means that you cannot believe in the prediction of general activity in this domain. So everything will be destroying there is no blocks, no rollers, you cannot measure time space and question is, is it final state?
So space-time disappear or it will be some continuation and this is open question.
시공간이 없어지거나 어떤 연속(시공간이 모두 합쳐진/엉켜있는 상태)이 있을 겁니다. 아직 풀리지 않은 질문이죠.
Black holes have an inside and an outside separated by a boundary called the event horizon. What is an event horizon? What does it look like, if it looks like anything at all? Let's explore this concept by revisiting what we mean when we talk about the surface of an object like the sun.
블랙홀은 사건의 지평선을 경계로 내부와 외부로 나뉜다. 관연 사건지평선은 무엇인가? 대체 어떤 모습일까? 이에 대한 답을 하기전에 먼저 태양 같은 항성의 표면을 살펴보기로 하자.
We often think of the sun, or any other star, as a big ball of gas which has a surface, but it's an oversimplification to say that all the star's gas lies inside this surface. Some of the sun's material is continually escaping from the hot and energetic surface.
우리는 태양같은 별을 표면을 가진 커다란 뜨거운 공이라고 생각한다. 하지만 그런 생각은 별을 구성하는 뜨거운 가스가 표면 아래에 갖혀 있다고 너무나 단순화 해서 보는 시각이다. 태양의 뜨겁고 강한 표면에서 물질들의 일부가 꾸준히 떨어져 나오는 중이다.
The solar wind pushes a small amount to the sun's gas, all the way to the outer edges of the solar system. This is the material that generates the auroras here on earth after all. For stars, we generally define the surface, known as the photosphere, to be the outermost layer of the sun. The photosphere is what we see when we look at the sun in visible light.
태양풍은 (태양의 자체질량에 비하면) 소량의 태양가스들을 태양계의 끝 넘어까지 불어내고 있다. 태양에서 불어오는 물질들이 지구에서 오로라 현상을 일으킨다. 별의 표면은 광구라고 하는데 가장 바깥쪽 껍질에 해당된다. 광구는 우리가 가시광선으로 보는 태양의 모습이다.
If we try to look deeper inside the sun, the hot gas blocks the light. So, we can't actually see deeper than the photosphere. Beyond the photosphere, there are additional regions of the sun where gas interacts, such as the chromosphere and the corona, but those layers are very faint and difficult to see.
태양의 내부를 보려고 해도 뜨거운 가스가 막아선다. 따라서 광구의 아래로는 실제로 볼 수 없다. 광구 밖으로 (뜨거운) 가스에 영향을 받은 층이 더 있는데 예를 들어 채층(chromosphere), 코로나 등이 있다. 하지만 이런층들은 매우 엷고 관측하기도 어렵다.
As you can imagine, saying exactly where the sun's surface is located, is a matter of scientific definition.
이처럼 여러 층에서 태양의 표면을 어디라고 말하는 것은 과학적으로 정의하기 나름이다.
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Although black holes do not have a surface, scientists have defined a boundary to separate the interior of the black hole from its exterior. A black hole's event horizon is a boundary that separates the black hole's interior which we are unable to see from the outer region.
비록 블랙홀이 표면을 갖고 있지 않지만 과학자들은 내부와 외부를 경계를 정의했다. 블랙홀의 사건의 지평선까지를 외부에서 들여다 볼 수 없는 블랙홀의 내부라 한다.
However, unlike stars, the black hole's event horizon is much easier to define because it's impossible for gas or light to escape from the event horizon. We say that the event horizon is the surface or boundary of a black hole, not as a rigid body but as the point of no return for material that has fallen in.
하지만 별과는 달리 가스든 빛이든 사건의 지평선을 넘을 수 없기에 블랙홀의 사건의 지평선(경계선 혹은 표면)을 정의 하기는 수월하다. 우리는 사건 지평선을 블랙홀의 표면 혹은 경계라고 한다. (명확히 형체를 구분할 수 있는) 강체는 아니지만 이 경계를 넘은 물질은 돌아올 수 없는 지점이기 때문이다.
Why isn't it possible to have a ball of gas inside of the event horizon?
사건의 지평선 안쪽은 왜 가스 공이 될 수 없을까? [별은 뜨거운 가스로 가득찬 공이다.]
It all comes down to a concept called hydrostatic equilibrium. In module two, we discovered that hydrostatic equilibrium is the balance between gravity and gas pressure in the interior of stars. Gravitational attraction tries to bring all the gas in the star towards the star's center, but gas pressure creates an outward force that prevents further gravitational collapse. When the stars are in balance, the star is stable and can stay the same size for a long time, like our sun.
그 이유는 바로 정역학 평형의 개념에서 찾을 수 있다. 2주차 강의 때 별의 내부에서 중력과 가스압 사이의 균형을 정역학 평형으로 설명하였다. 중심으로 뭉치는 중력과 밖으로 밀어내는 가스 압이 균형을 이뤄 중력붕괴를 막아 별이 안정적인 구의 모양을 유지한채 긴시간을 지낼수 있다.
Suppose we take a star and compress it into a smaller volume, overpowering gas pressure at the interior. The matter in the star will be squashed, and feel a stronger gravitational pull towards the center, which requires a larger gas pressure in order to push outwards to balance the star. Is it possible to continue compressing the star into smaller and smaller regions?
별을 한개 취해서 아주 작게 눌렀다고 하자. 내부 가스들은 과도한 압력을 받는다. 물질이 작은 부피에 몰리면 중심으로 강한 중력을 받는다. 별을 유지하기 위해 이를 떠받치려면 더큰 가스압이 필요하다. 별을 점점작게 뭉치도록 앞력을 계속 가할 수 있을까?
No. If you compress the star's gas within the star Schwarzschild radius, the gas pressure required to balance gravity becomes infinite. It's not possible to create infinite gas pressure, so gravity wins the battle and the star's gas will have to continue falling inwards It is impossible for any matter to be at rest inside of the black hole's event horizon.
만일 별을 슈발츠쉴트 반경 이내로 짜브러트린다면 이정도 중력에 균형을 이룰 가스 압이 필요하다. 무한한 가스압을 만들어 내기는 불가능하다. 따라서 가스 압과 경쟁에서 승리한 중력이 폭주하여 수축을 계속 하게 되므로 사건 지평선 안쪽에는 '정지해 있는' 어떤 물질도 없다.
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The event horizon can be understood by observing how light rays are bent by the gravitational field of a massive object. We know that if there is no gravity, light travels in straight lines, just like this ball rolling on a flat surface travels in a straight line. Just as the sheet is deformed by the presence of the weight, space-time is deformed by massive objects, like a star or a black hole.
무거운 천체의 중력장에 의해 빛이 휘는 정도를 관측함으로서 사건의 지평선을 이해할 수 있다. 중력이 없는 공간에서 빛은 직진한다. 만일 평면이 무게추에 의해 늘어진 것처럼 시공간은 별이나 블랙홀처럼 무거운 천체에 의해 변형된다.
When we roll a ball on the curved sheet, it doesn't travel in a straight line, instead, its path is curved towards the central mass. The closer the ball's starting point is to the mass, the more the path of the ball becomes curved. Light is deflected in the same way by the mass of a star or a black hole. If a star and a black hole have the same mass, deflection angle is the same for photons travelling on paths that are the same distance from the object, assuming the light path stays outside of the object.
휜 면에 공을 굴리면 직진하지 못한다. 대신 질량 중심을 향해 굽은 경로를 따라 움직인다. 공이 무게 중심에 다가갈 수록 더욱 굽는다. 빛도 같은 식으로 별이나 블랙홀에 의해 굽는다. 만일 별과 블랙홀이 질량이 같다면 그 천체에서 동일한 거리에 떨어져 외곽 경로로 움직이는 광자 굴절각도 같다.
We must remember that a black hole with the same mass as the star is much more dense. If you recall that the sun's radius is 700,000 kilometers, but a black hole with the same mass as the sun has an event horizon radius that is only three kilometers. This means that it's possible to get much closer to the center of a black hole than a star.
블랙홀이 별에 비해 매우 밀집되어 있다는 점에 주목하자. 같은 무게라도 별의 반경은 블랙홀의 사건 지평선에 비하면 매우 크다. 태양의 반경이 대략 7 십만 킬로미터에 달하지만 같은 질량의 천체의 사건지평선 반경 (슈발츠쉴트 반경)은 단 3킬로미터에 불과하다. 이 말은 (광자의 경로가) 질량 중심에 훨씬 가깝게 다가갈 수 있다는 뜻이다.
The radius of a non-rotating black hole is sometimes called the Schwarzschild radius, named after Karl Schwarzschild, the first person to solve Einstein's equations for strong gravitational fields.
비회전 블랙홀의 반경을슈발츠쉴트 반경이라 하기도 한다. 칼 슈발츠쉴르의 이름에서 따왔는데 그는 아인슈타인의 강한 중력장 방정식을 푼 최초의 인물이다.
Einstein's equations were thought to be so difficult that Albert Einstein himself said that nobody would ever be able to solve them. However, only a year after Einstein published the equations, Karl Schwarzschild found the first solution, which happened to describe a non-rotating black hole.
아인슈타인의 방정식은 너무 난해하다고 알려졌다. 알버트 아인슈타인 스스로도 아무도 풀지 못할 것이라고 말했을 정도다. 하지만 아인슈타인이 그 방정식을 담은 논문이 발표된지 채 일년만에 칼 슈발츠쉴트가 첫번째 해를 내놨다. 이해는 비회전 블랙홀의 설명에 적용되었다.
What a coincidence that Schwarzschild, whose name means black shield in German, was the first to describe the concept of a black hole.
독일어로 '검은 방패'라는 뜻을 가진 슈발츠쉴트가 블랙홀의 개념을 처음으로 설명한 것은 참으로 심상치 않은 우연이라 하겠다.
* 장방정식은 미분 방정식이다. 기하학과 물리량을 벡터 미적분(+텐서)을 도입하여 기술한 방정식이다. 언뜻 보면 무슨 이게 미분 방정식인가 하겠지만 축약 기술법으로 위아랫 첨자에 심오함이 잔뜩 담겨 있다. 구분 공간을 벡터 미적분과 기하학으로 기술한 것인데 이것 만으로도 어렵다. 게다가 미분 방정식 이라니! 미분 방정식은 원래 푸는게 아니다. 가설해를 상정해 놓거나 타당한 이유를 대고 근사화 해야 겨우 풀수있다. (죽기전 언제쯤 풀이를 이해라도 해보면 좋겠다!) 시험 문제에 나오는 미분방정식은 풀이 연습용으로 만든 아주 특별한 경우다.
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In module four, we explored the equation for Schwarzschild radius, which is two times the mass times G, over c squared. In this equation, Rs is the distance corresponding to Schwarzschild radius, M is the black hole's mass, G is Newton's gravitational constant, and c is the speed of light.
4주차 강의에서 슈발츠쉴트 반경에 관한 방정식을 다뤘었다. 블랙홀의 질량 M과 사건의 지평선 반경의 관계식이다.
For black holes that don't rotate, the event horizon is a sphere with a radius that is simply proportional to the black hole's mass. So, if you double the mass of a black hole, the radius of the sphere doubles, too.
회전하지 않는 블랙홀인 경우 사건의 지평선 반경은 질량중심에서 구의 반경으로 질량에 비례한다. 질량이 두배로 늘면구의 반경도 두배가 된다.
If you put numbers in for the sun, you'll find that the Schwarzschild radius is three kilometers. Physicists often simplify key equations by folding terms that occur repeatedly.
태양의 질량을 이식에 적용하면 슈발츠쉴트 반경은 3 킬로미터다. 물리 학자들은 상수들을 묶어 미리 계산해 놓고 익숙한 값을 반복적으로 사용하길 바란다.
In this case, the equation for the Schwarzschild radius is simplified so that it is equal to three kilometers, times the black hole's mass divided by the sun's mass. We now have the event horizon radius scaling with a ratio of masses, or in other words, it's dependent on how much more massive black hole is than the sun.
그래서 슈발츠쉴트 반경을 우리에게 익숙한 태양의 몇배라는 식으로 표현한다. 이렇게 해놓음으로서 사건의 지평선반경의 크기를 블랙홀 질량과 태양의 질량의 비율로 계산할 수 있다.
[미세한 물리상수와 천문학적 숫자들의 나열에 비해 엄청 편리하다. 게다가 이미 알려진 물리상수의 기호를 사용하지 않아도 된다. 기호를 쓰다보면 변수인지 상수인지 헛갈린다. 단순화 해놓으면 전체 그림이 보인다. 새로운 영감이 떠오를 지도 모르고....]
This is helpful as it makes the numbers a little easier. If we were to visit Cygnus X-1, which has a mass that is 15 times larger than the sun's mass, the radius of the black hole would be three kilometers times 15, which equals 45. Still pretty small.
시그너스 X-1의 질량은 태양의 15배 이므로 반경은 45킬로미터다. 역시 아주 작다.
The supermassive black hole at the center of the Milky Way has a mass that is 4 million times larger than our sun. This means that its event horizon is 12 million kilometers. That might sound like a big distance, but the largest black hole in our galaxy is smaller than the distance between our sun and Mercury.
우리은하 중심에 있는 블랙홀은 태양질량의 4백만배에 이른다. 사건지 평선의 반경은 1천2백만 킬로미터다. 얼핏 듣기에 아주 긴것 같아도 은하에서 가장큰 블랙홀이 태양과 수성 거리보다 짧다.
A black hole would need to have a mass that is 50 million times larger than the sun before the event horizon would be as large as the distance between the sun and the earth.
사건지평선반경이 태양과 지구사이 거리쯤 되려면 블랙홀의 질량은 무려 태양의 5천만배는 되어야 한다.
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Since the event horizons of supermassive black holes are further away from the black hole center, the tidal forces at the event horizon are smaller for black holes with larger masses. As we learned earlier, tidal forces can be pretty hazardous to an astronaut's health. This means that if you get to choose which black hole to visit, you should choose a larger black hole mass. It is estimated that a black hole should be at least one thousand solar masses in order to be safe to visit.
초거대 블랙홀의 사건지평선은 중심에서 멀리 떨어져 있기 때문에 조석력이 작다. [조석력은 중력에너지 차에서 나온다. 중력가속도는 거리의 세제곱에 역비례하므로 중력에너지 차도 그만큼적다.] 이미 알고 있겠지만 조석력은 우주비행사에게 치명적이다. 안전하게 블랙홀 여행을 하려면 태양질량의 1천배 이상되는 블랙홀을 골라 방문해야 한다.
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Since the radius of a black hole is proportional to its mass, if matter falls into the black hole, the event horizon grows larger. In most cases, this is incredibly small change. However, if two black holes collide, they can merge into one significantly larger black hole. In case you're wondering, Stephen Hawking proved that it's impossible for a black hole to split into multiple black holes. We'll talk more about this in module seven.
블랙홀의 반경은 질량에 비례하므로 물질들이 빨려들어 갈수록 사건 지평선의 범위는 넓어진다. 대부분 경우 변화량은 아주 작다. [사건지평선이 급격히 늘만큼 빨려들어가는 물질이 순식간으로 많지 않다.] 하지만 블랙홀이 충돌하면 한개의 거대블랙홀로 합쳐진다. 의구심이 들텐데 [두 블랙홀이 근접하면서 생긴 엄청난 조석력은 블랙홀을 산산조각 내지 않을까?] 스티븐 호킹은 여러개의 블랙홀로 쪼개질 수 없음을 증명해 보였다. 이에 대해서는 7주차 강의에서 다룬다.
If we shine a flashlight in the direction of a black hole, the closer the light is aimed towards the black hole, the more curved the light beam will become. As we aim a flashlight closer and closer, we discover that there's a special distance at which light from our flashlight begins traveling in circles around the black hole. This is an area called the photon sphere, which corresponds to a radius that is one and a half times larger than the radius of the event horizon.
블랙홀을 향해 손전등을 비춰보자. 블랙홀에 가까이 갈수록 빛줄기는 더 많이 휜다. 점점더 가까이 가다 어느 지점에 빛이 블랙홀의 주위를 돌게 된다. 이 지점을 광자구(photon sphere)라 한다.광자구의 반경은 사건 지평선 반경의 1.5배다.
The photon sphere is similar to the innermost stable circular orbit for particles, except that circular photon orbits are unstable. If a photon becomes trapped within the photon sphere, only a small nudge is enough to kick photons away from the black hole or to send them spiraling inward.
광자구는 입자의 최근접 안정 원궤도(ISCO; 이스코)와 비슷하다. 하지만 광자의 궤도는 매우 불안정하다. 광자가 광자구에 진입 했더라도 약간의 자극에도 광자는 블랙홀에서 벗어나거나 안쪽으로 뛰어든다.
Scientists call this collection of circular photon orbits the ring of fire. In this computer simulation, a black hole is surrounded by the purple and red accretion disk. Some of the light emitted by the accretion disk, travels close to the black hole and becomes trapped in circular orbits for a while before escaping. An observer would see these escaping photons forming a bright ring around the black hole.
과학자들은 광자의 원궤도를 Ring of Fire(불의 환) 라고 한다. 컴퓨터 시뮬레이션에서 보면 블랙홀이 적색과 보라색으로 표현된 강착 원반에 둘러싸여 있다. 강착 원반이 블랙홀을 향해 안으로 돌다가 잠시 원궤도를 그리다가 빠져나간다. 이렇게 빠져나가는 광자들이 블랙홀 주변의 밝은 원을 형성 할텐데 우리는 이를 관측할 수도 있을 것이다.
Current telescope technology is on the verge of capturing images of a photon sphere. New telescopes like the Event Horizon Telescope and others in development should be able to capture images of the ring of fire.
현재 망원경 기술은 광자구의 영상을 찍을 수 있는 수준에 거의 다달았다. 사건지평선 망원경 (Event Horizon Telescope) 또는 개발 중인 새로운 망원경들은 (조만간) 불의 환 영상을 얻을 수 있으리라 기대된다.
If we aim our flashlight closer to the black hole than the circular photon orbit, photons emitted from the flashlight will move on plunging orbits that will end up crossing the event horizon. Any light entering the event horizon is unable to escape. If we can image the region outside the event horizon of a black hole, we would see a region with no light emission, that is sometimes called the black hole shadow.
손전등을 광자 궤도보다 좀더 블랙홀에 가깝게 비추면 전등을 떠난 광자들은 사건 지평선을 넘어 빨려 들어간다. 사건지평선 밖으로 어떤 빛도 빠져나오지 못한다. 만일 블랙홀의 사건지 평선 밖의 영역의 사진을 얻는다면 그 영역을 블랙홀의 그림자라 한다. [불의 환과 사건의 지평선 사이의 검은 영역]
What will happen to an astronaut that is far from the black hole? Let's consider a situation in which both an astronaut and a distant observer are equipped with flashlights capable of emitting one pulse of light per second. If they shine these pulsing flashlights at one another while the astronaut falls towards the event horizon, what observations would we expect them to see?
블랙홀에서 멀리 떨어진 우주비행사에게 무슨 영향이 있을까? 우주 비행사와 멀리 떨어진 관측자 각자가 매초마다 반짝이는 손전등을 가지고 있다고 하자. 두사람이 서로 반짝이는 손전등을 서로 비추고 있고 우주 비행사는 사건의 지평선을 향해 떨어지는 중이다. 멀리 있는 관측자는 우주비행사의 손전등이 반짝이는 걸 볼 수 있을까?
We already learned that gravitational time dilation will stretch the time intervals that the faraway observer sees. As the astronaut falls into the event horizon, the time interval between the pulses received by the observer stretch to infinite amounts of time, even though the astronaut may have only spent a few hours falling into the black hole.
앞서 얘기했듯이 중력 시간 평창으로 인해 멀리 있는 관측자는 우주비행사의 손전등이 반짝이는 시간이 아주 늘어지는 걸 보게 된다. 우주비행사가 사건의 지평선에 떨어지면 반짝임 간격이 무한정 길어지는 걸 보게된다.
Since the event horizon is a one-way street in space-time, the astronaut falling towards the black hole will continue receiving signals from a distant observer at exactly the same rate of one pulse per second. The astronaut even continues to receive the signals after crossing the black hole's event horizon. Remember, the event horizon is asymmetric, just like one-way street. Light can enter the black hole, but it can't escape.
사건의 지평선은 시공간에서 일방통행로와 같다. 블랙홀로 떨어지는 우주비행사는 관측자가 보내는 신호를 매초 정확하게 받는다. 심지어 우주비행사는 블랙홀의 사건지 평선을 넘으면서도 받는 신호는 여전하다. 기억할 점은 사건지평선이 비대칭 이라서 일단 들어온 빛은 나가지 못한다.
The in-falling light pulses from the distant observer don't change as they pass through the event horizon to be observed by the astronaut. Just as there is no wall of gas left over from us compressing a star, there's nothing special marking location of the event horizon.
우주비행사가 받은 멀리 있는 관측자가 보낸 떨어지는 빛의 깜박임은 사건의 지평선을 넘을 때도 변함이 없다. .......
This makes a trip to a black hole extremely dangerous. If you manage to survive the tidal forces near a black hole, it is easy to accidentally crossover the event horizon since it seems like an unremarkable location in space when you're traveling through it. So, if you do travel to a black hole, be sure to calculate exactly where the event horizon is before you approach.
블랙홀로 떨어지는 우주비행사는 외부의 신호에 이상한점(시간의 팽창 같은)을 인지하지 못한다는 점은 블랙홀 여행에서 아주 위험하다. 블랙홀 근처에서 조석력을 견딘다 해도 우주에는 어떤 위험표지도 없기에 실수로 사건지평선을 넘을 수 있다. 만일 블랙홀에 구경갈 참이라면 사건지평선이 어디쯤인지 정확히 계산했는지 확인하자.
We know that anything entering a black hole's event horizon cannot escape. Not even light. This means that you can't sneak a look at what's inside and let people outside know what's happening. While you obviously wouldn't risk putting your head into a black hole, if you're sitting inside your rocket orbiting just outside the event horizon, you could lower a camera past the event horizon. However, in order to take a picture of the inside of a black hole, the electrons in the camera would need to travel faster than the speed of light to send any information back up to your spaceship. We expect that the structure holding the camera will be ripped apart, and that the camera would fall inwards before any photos could be taken.
블랙홀 내부가 궁금하다고 고개만 들이 밀어도 않된다. 사건지평선 밖의 궤도를 돌면서 카메라만 들이 밀수도 있겠지만 카메라의 전자들이 빛보다 빨라야 사진을 건질 수 있다. 사진이 도착하기 전에 카메라 몸체가 박살나 잔해들은 벌써 빨려 들어간다.
Even though we can't, in theory, pass information about the interior of a black hole past the event horizon, we can deduce some of the properties of a black hole's interior. One object theorized to exist by Sir Roger Penrose is called the singularity, an object so foreign to the laws of physics that our understanding of them is incomplete.
이론적으로는 사건의 지평선을 통과하여 블랙홀 내부의 정보를 전달 할 수 없지만 블랙홀 내부의 특성을 짐작할 수는 있다. 그 한가지 대상을 '특이점'이라 하는데 로저 펜로스 경에 의해 이론적으로 입증되었다. [블랙홀 내에 뭔가 있다!] 인간이 알고 있는 모든 물리법칙들이 붕괴된다. [시간이 멈춰있으니까!] [특이점]
Singularities are thought to be such dreadfully ugly objects that we think the event horizons themselves are there to shield us from seeing it. This yet unproven conjecture is sometimes called Cosmic Censorship Hypothesis, and we will go into more gory detail in the next section.
특이점은 아주 기묘한 대상(장소)인데 우리가 속을 드려다 볼 수 없게 스스로 장막을 두르고 있다. 아직 풀리지 않은 이 수수께끼를 '우주 검열 가설'이라고 한다. 다음 강의에서 이점에 대해 아주 세세히 다뤄 보겠다.
