How does time dilation apply at the centre of a black hole?

Physics Asked on May 9, 2021

At the direct centre of a black hole, you have $0$ GPE, and the net gravitational force is $0$. So how does time dilation work there (or is this another physics mystery)?

Specification: I refer to how the time dilation changes from the actual surface of the black hole to the centre (I suspect it will continue to increase, but in a different way)


One Answer

There is no "center of a (Schwarzschild) black hole" in a traditional sense. At the horizon, the schwarzschild "radial" direction switches from spacelike to timelike, and the singularity becomes more a "time in the future" than a "place you can go to".

Also, arguments like this about potential energy don't generalize well from Newtonian mechanics, and to the extent that you can use them, you have to use the relativistic generalizations of them, which involve terms that look like $1 - frac{2M}{r}$, which is infinite for $r=0$

Correct answer by Jerry Schirmer on May 9, 2021

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