# Why doesn’t light escape a black hole? [duplicate]

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).

• My sources: Wikipedia, NASA’ website, National Geographic’s site, Vsauce (1-3), kursgezagt-in a nutshell. May 8, 2019 at 19:28
• 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.
– user4552
May 8, 2019 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. May 8, 2019 at 20:16
• 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. May 8, 2019 at 20:52
• Possible duplicate of Why is a black hole black? May 9, 2019 at 5:48

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.