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A black hole is a region of spacetime from which nothing can escape. More formally, the future light cone of any observer within the black hole is completely contained in the black hole, and the black hole region is not within the past light cone of any observer that goes to spatial infinity in an infinite amount of time.
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Can you exit the event horizon with a rocket?
The reason given in most places about why one cannot escape out from an event horizon is the fact that the escape velocity at the event horizon is equal to the speed of light, and no one can go faster …