If I asked you who first proposed the idea of a Blackhole, who would be your first guess? Perhaps Albert Einstein, Stephen Hawking or Karl Schwarzschild. While these scientists have had a huge impact on black hole astrophysics, the idea of a strong gravitational field altering light was first described by an often overlooked clergyman named John Michell.
처음 블랙홀을 생각해낸 사람은 누구라고 생각하세요? 알버트 아인슈타인, 스티븐 호킹, 칼 슈발츠쉴트. 이 과학자들은 블랙홀 천체물리학에 지대한 공헌을 했습니다만 처음 강한 중력장이 빛의 경로를 변경하게 만들거라는 생각을 한 이는 영국의 목사 존 미첼이라는 사실을 간과하는 경향이 있습니다.
John Mitchell was the first to describe an object whose escape velocity exceeded the speed of light, which he called "Dark Stars." The year was 1783, falling very close to the midpoint between Newton's theory of universal gravitation and Einstein's theory of special relativity. John Michell, a retired professor of geology at Cambridge was working as director of Thornhill in England, and he used his spare time to fuel his scientific curiosity, in particular, working with theories of light and gravity.
존 미첼은 탈출 속도가 빛보다 빠른 별이 있을 수 있다는 생각을 했는데 이런 별을 검은 별(Dark Star)라고 했죠.1783년은 뉴튼의 만유인력과 아인슈타인의 특수 상대론 사이에 위치합니다. 존 미첼은 캠브리지에서 지질학을 가르치다 은퇴하고 잉글랜드에서 감독관으로 일했죠. 그는 여가시간에 과학의 호기심을 푸는데 보냈죠. 특히 빛과 중력에 관한 이론에 관심이 많았습니다.
John supposed that light consisted of a particle, which was a topic of hot debate at the time, and that gravity acted upon the particles of light in the same way that gravity acts on all objects.
존은 빛이 입자라고 생각했습니다. 그당시 아주 뜨거운 논쟁꺼리였죠. 중력이 다른 물체처럼 빛 입자도 끌어들인다는 이론입니다. 하지만 실험적인 증거는 없었습니다. 다만 뉴턴의 중력이 만유인력, 빛 입자 조차 끌어들이는, 이라는 거죠.
At the time, there was no experimental evidence to think otherwise and Newton's gravity was considered a universal law. Rector Michell reasoned that objects within a gravity well require a certain amount of speed to reach infinity, the speed which we now call escape velocity. And that for particularly small and dense objects, the escape velocity might exceed the speed of light.
교구 목사였던 미첼은 중력우물 내의 물질은 무한 속도에 도달하기위해 일정량의 속도를 가져야 한다는 근거를 제시했는데 바로 탈출속도라는 겁니다. 그리고 특히 작으면서 아주 밀집된 물체의 경우 탈출 속도가 빛의 속도를 넘어 서는 그런 물체(별) 이 있을 수 있다는 생각을 했죠.
The French mathematician, Pierre-Simon Laplace, came up with the same idea in 1796, which he referred to as an "invisible body." Although Laplace first wrote about invisible bodies in 1796, more than ten years after Michell, this idea was probably developed independently since there was very little scientific communication between France and England in that period.
프랑스의 수학자 피에르 시몬 라플라스는 1766년에 비슷한 생각을 했습니다. 그는 "보이지 않는 물체"라고 했죠. 라플라즈가 보이지 않는 물체를 언급한 것은 10년 후 이나 그당시 영국과 프랑스사이에 과학적 교류가 매우드믄 시기이므로 서로 독립적인 생각이었다고 하겠습니다.
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Let's have a look at the escape velocity equation again, but this time let's do something silly. Instead of solving for the velocity, V_e, let's solve where the radius of an object with mass m whose escape velocity is equal to the speed of light, just as rector Michell did. We'll denote the speed of light as the letter c and use it to replace V_e. In order to solve for the radius r, we need to first square both sides of the equation so that C becomes C squared and the square root sign on the right hand side goes away, and then we can multiply both sides of the equation by a factor of r divided by C squared, leaving us with the solution in terms of the radius.
미첼이 그랬던 것 처럼 탈출속도가 빛의 속도인 별을 생각해 보자. 앞서 계산해 본 탈출 속도식에 적용하면 질량 M이 매우 작은 반경 r에 집중된다. 밀도가 극히 높은 별이 된다.
A body of mass M has an escape velocity equal to the speed of light when its radius r is equal to 2GM divided by C squared. So what this means is that an object of mass M, we can calculate how small it would need to be in order to have an escape velocity equal to the speed of light.
Let's try Earth's mass for fun. Inserting M equal to 5.972 times 10 to the 24 kilograms into the equation, yields a radius of a puny 8.87 millimeters, like a tiny ball less than one centimetre on a side. So if a ball weighed the same as the entire Earth, it would have an escape velocity equal to the speed of light at its surface.
Our Sun's escape velocity is 617.7 kilometers per second given a solar mass and the average solar radius. In order for the sun's escape velocity to increase to the speed of light or 300,000 kilometers per second, it's radius would have to be reduced from 695,700 kilometers to a radius smaller than 2.953.
What would the sun look like if it were compressed to 2.953 kilometers? With its escape velocity equal to the speed of light, light would no longer escape from it, so the sun would appear dark. Also, any light falling towards the sun would disappear completely the moment it crossed the sun's dark surface. In fact, nothing could escape from the object's surface because we know that the speed of light is in upper limit in our universe.
만일 태양의 크기가 2.953 킬로미터로 줄어들면 어떻게 보일까? 탈출 속도가 빛의 속도와 같아 진다면 태양에서 빛이 빠져나오지 못해 검게 보일 것이다. 또한 태양으로향하던 모든빛도 빠져나오지 못한다. 빛은 우주의 최고속도 이므로 빛이외 그어떤 것도 빠져나오지 못한다.
Using only classical physics, Michell was the first to describe dark stars by trying to determine a method for measuring the distance and brightness of stars. Instead, he invented the first description of a black hole, an object massive enough to prevent light from escaping it. Additionally, Michell also predicted one of the most interesting results in black hole physics.
You see, the equation that we naively replaced escape velocity for the speed of light, with that equation comes up again once we encounter Einstein's general relativity as a solution for the event horizon of the simplest kinds of black holes, Schwarzschild black holes.
위의 식에 봤듯이 단순히 탈출속도에 빛의속도를 적용한 것처럼 , 아인슈타인의 일반상대론 공식에 적용하여 아주 단순한 형태의 블랙홀의 사건의 지평선의 반경을 구할 수 있다. 이 단순한 블랙홀을 슈발츠쉴트 블랙홀이라 한다.
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