3 ms·

We also know GR is incomplete because it cannot explain what happens in a black hole at the singularity. Objects within have to always be approaching it but nev

by XorNot 3y ago

We also know GR is incomplete because it cannot explain what happens in a black hole at the singularity. Objects within have to always be approaching it but never reach it (since then they would not be approaching it) but it has a finite volume in space, so they must eventually get there.

ben_w 3y ago
Black holes have a finite volume on the outside, but I'd have to do an integral above my skill level to work out the volume inside; if I understand right, the radial direction and the time direction switch roles at the event horizon. Also, I'm not sure you need stuff to always approach without ever getting there: it's not clear what happens to quantum fields at a singularity, but if you no longer have time displacement symmetry you don't get energy conservation so stuff might just cease to exist.
- nyssos 3y ago
  > but I'd have to do an integral above my skill level to work out the volume inside; if I understand right, the radial direction and the time direction switch roles at the event horizon. If you try to naively apply the same procedure you would use to define volumes outside the event horizon, it's proportional to the lifetime of the black hole (infinite in the classical case) for the reason you note. Of course the better way to interpret this is probably just that the interior volume of a black hole is ill-defined.
evanb 3y ago
I think you're making an error---according to GR the singularities in black hole cores are in time, not locations in space, as confusing as that is, and as much as colloquial language suggests it. Every geodesic that crosses the horizon terminates at the singularity in a finite amount of time. If you fall past the horizon the singularity is in your definite future and in a finite amount of proper observer time your geodesic will end, at which point ... who knows what happens.

by XorNot 3y ago

ben_w 3y ago

Black holes have a finite volume on the outside, but I'd have to do an integral above my skill level to work out the volume inside; if I understand right, the radial direction and the time direction switch roles at the event horizon. Also, I'm not sure you need stuff to always approach without ever getting there: it's not clear what happens to quantum fields at a singularity, but if you no longer have time displacement symmetry you don't get energy conservation so stuff might just cease to exist.

nyssos 3y ago
> but I'd have to do an integral above my skill level to work out the volume inside; if I understand right, the radial direction and the time direction switch roles at the event horizon. If you try to naively apply the same procedure you would use to define volumes outside the event horizon, it's proportional to the lifetime of the black hole (infinite in the classical case) for the reason you note. Of course the better way to interpret this is probably just that the interior volume of a black hole is ill-defined.

evanb 3y ago

I think you're making an error---according to GR the singularities in black hole cores are in time, not locations in space, as confusing as that is, and as much as colloquial language suggests it. Every geodesic that crosses the horizon terminates at the singularity in a finite amount of time. If you fall past the horizon the singularity is in your definite future and in a finite amount of proper observer time your geodesic will end, at which point ... who knows what happens.