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

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)

Related:

https://physics.stackexchange.com/a/251020/182917

• There is no "actual surface" of a black hole. There's an event horizon, but it is not a physical surface. Apr 14, 2021 at 16:55

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 $$r=0$$