the four-dimensional spacetime

[Gamling]

right, so, i was wondering: as we all know theory has it that in a black hole there is no time present, as the matter withing is caged in singularity. I was wondering: as we know, black holes have a volume, meaning that the matter within has to exist in the three dimensions of space: put no matter how many singular objects together, the result will still not be something in 3D. nlow then that would proof that matter within a black hole would indeed be compressed, but not to a point of total singularity.
can something cease to exist in one dimension (time) and continue to exist in the other three?

or would that merely mean, that time runs very slowly in a black hole?

[marnix]

surely the fact that a black hole can be described as a singularity doesn't mean it can't have size ?

[Gamling]

why, if something is singular that means that it has less dimensions that a string which would be 1D so to speak: one axis upon which a point can move. if something is in singularity even that axis is gone, all that is left is a point (dot? whatever, I dunno all the english terms). as a point doesn't have any circumference meaning that no matter how many you add, the result is still 0 (like adding a zillion 2D plains and still not getting any thickness...

[marnix]

no it doesn't : a singularity implies the existence of a point at which some properties moves towards infinity, in this case the space-time curvature
the event horizon or Schwarzschild radius depends on the mass of the black hole, and defines its size

[Gamling]

i dunno, wikipedia says:

Gravitational singularity, a point in spacetime in which gravitational forces cause matter to have an infinite density and zero volume

that does sound like a singularity soesn't have any definite volume and therefore the schwarzschild radius wouldn't be the size of the singular objects.

the schwarzschild radius doesn't really define the circumference of a black hole, does it? only the event horizon. but not the actual volume!?

[marnix]

that's probably why physicists don't like singularities - the impression is that it is a mathematical construct that it is the result of our inability to truly grasp the essence of a black hole, and doesn't reflect its true physical behaviour

[Gamling]

so you agree on that account?

[marnix]

let's say i reserve judgement and give a provisional nod of agreement

[Gamling]

*groans in defeat* you're impossible 

[marnix]

i do my best