# Relativity and volume of black hole

Does Einstein's theory of special or general relativity incorporate volume?

In a particle accelerator two particles smash together at relativistic speeds and "create" new particles (quarks etc) due to $E=mc^2$. In our space-time, the volume needed for these new clumps of mass already exists in local space-time.

What happens in the super-dense core of a galaxy where stars and black holes are all sucked together into a super-dense object? Presumably, all the matter has been compressed to its theoretical limit. When another super-dense object (another black hole) strikes it at relativistic speeds, where does the volume come from to accommodate the creation of these new particles? If space-time of a black hole is infinitely curved, how can new volume be created for these particles to occupy?

• I'm not sure why this question has attracted the 3 close votes it has. It's a good question that is being actively researched (search ADS for BH-BH mergers, if you don't believe me). – Kyle Kanos Jul 11 '14 at 0:09

On paper, a black hole already has infinite density. Two coalescing holes would combine to another object of infinite density.

Realistically, we would need quantum gravity to prevent a true singularity from forming,a nd there, we could address, more concretely, what happens when the "masses" in the center of the black holes merge. But until we unambiguously have a true theory of quantum gravity, we can't answer this.

And yes, you can compress two stars together enough in a collision that they will collapse to a black hole.

• As an aside, BH-BH mergers are one of the primary suspects for gamma-ray bursts (at least for large redshifts); see this recent paper. – Kyle Kanos Jul 11 '14 at 0:07
• @KyleKanos: the link says that NS-NS and NS-BS mergerrs are the suspects, which makes sense, since you need charged matter to generate GRBs. – Jerry Schirmer Jul 11 '14 at 0:09
• Yes, NS-NS & BH-NS mergers are also candidates for GRBs. However, figures 3 & 4 of the link show the merger rate density for BH-BH events as significantly larger than the others (except for the case of High BH kicks, which destroys the binary system so the rate should be lower). – Kyle Kanos Jul 11 '14 at 0:14
• THe merger rate is higher, but they aren't GRB candidates, because there is no coupling to the EM field. They are expected to dominate the space of LIGO sources, though. – Jerry Schirmer Jul 11 '14 at 12:47
• Hmm, I could have sworn that BH-BH mergers were expected precursors for long duration GRBs, but the several papers I've pulled up on GRB precursors only involve NS-NS or NS-BH mergers. Thanks for helping me do some investigation! – Kyle Kanos Jul 11 '14 at 13:14

If space-time of a black hole is infinitely curved, how can new volume be created for these particles to occupy?

The spacetime of a black hole isn't infinitely curved. Only at the spacetime singularity within a black hole is the curvature infinite.

The spacetime near, at, and within the horizon is highly curved but not infinitely so.