# References for larger black hole behind the horizon of a smaller black hole

Some time back, I attended a talk which claimed that behind the horizon of a black hole, it is possible to embed a much larger black hole, i.e. it possesses a larger horizon area. The speaker showed some constructions with BTZ black holes where they embedded a BTZ black hole with a much larger area behind the horizon of a smaller BTZ black hole. There was another claim that one could embed more of such black holes as well.

Unfortunately, I have not been able to locate any references regarding the same, neither recollect the speaker's name as well. It will be very helpful to me if a few references are put forward in this regard.

• Just to clarify for those unfamiliar - you do mean "inside the event horizon sphere" , right? Apr 13 '21 at 15:28
• I suspect this situation can occur because a black hole is "bigger on the inside" due to GR rules about warping of space. Apr 13 '21 at 15:37
• @CarlWitthoft Yes, you are correct, I meant inside the event horizon. Can you elaborate a bit more about your description? Apr 13 '21 at 16:50

It is likely that the talk was about multiboundary wormhole/black hole geometries in (2+1)–dimensional gravity.

Remember that BTZ black hole could be seen as a factor space of $$\text{AdS}_3$$ spacetime by a discrete group of isometries generated by a single element. Multi-black hole geometries are factors $$\text{AdS}_3/Γ$$ by more complex discrete subgroups $$Γ$$ of isometry group.

It is possible to think about such geometries in terms of initial data on a slice $$t=0$$, which would be a fundamental domain of hyperbolic plane $$H^2$$ under the action of $$Γ$$:

An more detailed introduction could be found in this blogpost by Shaun Maguire

While such solutions are known for more than 20 years [$$1$$], recently they attracted attention as an important model to understand entanglement entropy within holography [$$2$$] and as a realization of $$\text{ER} = \text{EPR}$$ conjecture [$$3$$].

Note, that I would argue against statements that second (and third etc.) black hole is inside the event horizon of the first black hole, “behind” would probably be more accurate, since the “world” with second black hole is “hidden” by the horizon of the first (just like the “left” asymptotic region of Kruskal–Szekeres extended solution is hidden from the “right” asymptotic region), but the interior proper of the first black hole does not contain the second.

References

1. Brill, Dieter R. Multi-black-hole geometries in (2+ 1)-dimensional gravity. Physical Review D 53.8 (1996): R4133, doi:10.1103/PhysRevD.53.R4133, arXiv:gr-qc/9511022.

2. Maxfield, H. (2015). Entanglement entropy in three dimensional gravity. Journal of High Energy Physics, 2015(4), 31, doi:, arXiv:1412.0687.

3. J. Maldacena and L. Susskind, Cool horizons for entangled black holes, Fortsch. Phys.61(2013)781–811, doi:10.1002/prop.201300020, arXiv:1306.0533.

• Thank you for the answer. You are right, the terminology for this case should be "behind" instead of "inside". Just wanted to confirm, say for a 3-boundary womhole, the horizon sizes are not fixed, and can be arbitrary right? Apr 13 '21 at 21:40
• Also thank you for the nice links, will devote some time to go through them. Apr 13 '21 at 21:44
• @MichaelWilliams: the horizon sizes are not fixed, and can be arbitrary right Yes, masses could be arbitrary. Apr 14 '21 at 18:50
• Thank you very much. :) Apr 14 '21 at 19:38