I always think that it is not possible to escape from within event horizon. However, some one recently told me with deep conviction that it is possible with sustained energy output. I countered with calculations in Schwarzschild metric showing that any objects below event horizon in the simplistic black hole will hit the singularity within a finite proper time, and was met with the response that Schwarzschild metric was a bad choice for coordinate system.
Now I understand that the singularity at $r=\frac{2GM}{c^2}$ in Schwarzschild metric is an artifact of the coordinate choice, and thus it seems that he could have a point. So my question is, can one prove that it is (or not) possible to escape from within the event horizon of a simple static black hole using a better metric?
Answer
See Why is a black hole black?
It's quite true that the Schwarzschild coordinates misbehave near the horizon, but there are plenty of other coordinate systems we can use. My answer to the question I've linked above uses Gullstrand-Painlevé coordinates, but you can also use Eddington-Finkelstein or Kruskal-Szekeres coordinates. The conclusion is the same in all coordinate systems - once you have crossed the event horizon there is no way back.
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