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When an object is squeezed to its Schwarzschild radius it becomes a black hole (made by density) and its mass does not change (its gravity doesn’t change), but if its mass doesn’t change (its gravity doesn’t change) how does light not escape the black hole? The question is not why a black hole is black, or why light does not escape black holes in general. The question is why light does not escape a Schwarzschild black hole with a small mass (which, presumably, means the gravitational pull does not change either).

PokéKingFlames
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  • My sources: Wikipedia, NASA’ website, National Geographic’s site, Vsauce (1-3), kursgezagt-in a nutshell. – PokéKingFlames May 08 '19 at 19:28
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    When an object reaches the swartzschild radius it becomes a black hole Not really. What do you mean by this? (made by density) What does this mean? but if it’s mass doesn’t change (it’s gravity doesn’t change) how does light not escape the black hole? This seems like a non sequitur. –  May 08 '19 at 20:08
  • The “made by density” means it’s density alone made it, nothing else, not because it is a star that is out of fuel or anything else. – PokéKingFlames May 08 '19 at 20:16
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    If the Sun suddenly collapsed into a black hole, we would feel no change in its gravity field here on Earth. But, the strength of the gravity field is inversely proportional to the square of your distance from the center of mass. In its present form, you can come no closer than about 700,000 km to the Sun's center of mass before you enter the Sun itself. But, you could get as close as 3 km to the center of the Sun-as-black-hole and still be outside its Swarzchild radius. At that distance, the gravity would be around 54 billion times stronger than gravity at the surface of the Sun today. – Solomon Slow May 08 '19 at 20:52
  • @BenCrowell Aren't most physics paradoxes "non sequitur"? Many "paradoxes" have an incorrect assumption in the problem statement (e.g. the twin paradox). I'm not sure if that is a valid concern. –  May 08 '19 at 23:35
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    Possible duplicate of Why is a black hole black? – John Rennie May 09 '19 at 05:48
  • Your recent edit doesn't change the answer to your question. A Schwarzschild black hole with a small mass is still a black hole. – PM 2Ring Jul 12 '19 at 06:12
  • @PM2Ring The question was not if such a black hole is a black hole, NO, it was why light does not escape such a black hole. – PokéKingFlames Jul 12 '19 at 19:48
  • Light doesn't escape from such a black hole for the same reason it can't escape from any black hole: the spacetime geometry inside a black hole doesn't contain any worldlines that in the futureward direction lead out of the event horizon. How the black hole happened to form is irrelevant. – PM 2Ring Jul 12 '19 at 19:56
  • @PM2Ring If you are confident in your answer put it in the answer bar, not the comments. – PokéKingFlames Jul 20 '19 at 15:45
  • As far as I'm concerned John's answer to the linked answer answers your question. Besides, this question is currently closed, so I can't post an answer to it. If you want it to be reopened, you need to explain why John's answer doesn't cover your question. If you can do that, then people may vote to reopen this question. – PM 2Ring Jul 20 '19 at 15:54

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The problem I think is that you are assuming that the force of gravity is given by

$$F=G\frac{m_1m_2}{r^2}$$

that is, Newtonian gravity. You are assuming that the value of $F$ on a new material will also remain constant, despite the fact that the black hole should have just gained mass. I'm unsure why you think gravity not changing is a definite proof that light won't escape, but perhaps if I can help you find a flaw in your logic, you will be able to solve it for yourself. The equation above is a useful approximation not near a blackhole. Near a blackhole, we reach what is called Schwarzchild spacetime and we must deal with things accordingly. When an object reaches the Schwarzchild radius, it does not become a black hole. It must first reach the singularity which takes some time after reaching the Schwarzchild radius. The mathematics are understandable to undergraduate students: in this sense, I just mean that even with a few university math courses under your belt, you should at least to some degree be able to follow the derivations. I suggest reading Black Holes: An Introduction the Second Edition by Derek Raine and Edwin Thomas if you are truly interested in understanding why Newtonian gravity is not a viable option here.

I think the above is a solid response to set you on your way, but the truth is simply that if you think of gravity intuitively, it usually works; but when you are discussing black holes, this intuitive approach fails.

Kraigolas
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