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How big is a black hole? · Around

2014

How big is a black hole?

Christodoulou, Marios, Rovelli, Carlo

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The 3d volume inside a spherical black hole can be defined by extending an intrinsic flat-spacetime characterization of the volume inside a 2-sphere.

For a collapsed object, the volume grows with time since the collapse, reaching a simple asymptotic form, which has a compelling geometrical interpretation.
Perhaps surprising, it is large.
The result may have relevance for the discussion on the information paradox.

Built on

W. Ballik and K. Lake, “Vector volume and black holes,” Physical Review D
Original
1935
Earlier work this paper cites.
F. Estabrook, H. Wahlquist, S. Christensen, B. DeWitt, L. Smarr, and E. Tsiang, “Maximally Slicing a Black Hole,” Physical Review D
1973
Earlier work this paper cites.
R. Bousso, “A covariant entropy conjecture,” Journal of High Energy Physics
1999
Earlier work this paper cites.

Similar

M. Parikh, “Volume of black holes,” Physical Review D
2006
Cited alongside, same era.
B. S. DiNunno and R. A. Matzner, “The volume inside a black hole,” General Relativity and Gravitation
Original
2009
Cited alongside, same era.
D. Grumiller, “The Volume of 2D Black Holes,” arXiv:0509077 [gr-qc]
Cited in the paper.
W. Ballik and K. Lake, “The volume of stationary black holes and the meaning of the surface gravity,” arXiv:1005.1116
Original
Cited in the paper.
G. W. Gibbons, “What is the Shape of a Black Hole?,” arXiv:1201.2340
Original
Cited in the paper.
S.A. Hayward“Formation and evaporation of non-singular black holes,” arXiv:gr-qc/0506126
Cited in the paper.
C. Rovelli and F. Vidotto, “Planck stars,” arXiv:1401.6562
Original
Cited in the paper.
H. M. Haggard and C. Rovelli, “Black hole fireworks: quantum-gravity effects outside the horizon spark black to white hole tunneling,” arXiv:1407.0989
Original
Cited in the paper.
A. Barrau and C. Rovelli, “Planck star phenomenology,” arXiv:1404.5821
Original
Cited in the paper.
A. Barrau, C. Rovelli and F. Vidotto, “Fast Radio Bursts and White Hole Signals,” arXiv:1409.4031
Original
Cited in the paper.
A. Perez, “No firewalls in quantum gravity: the role of discreteness of quantum geometry in resolving the information loss paradox,” arXiv:1410.7062
Original
Cited in the paper.
E. Bianchi, “Black hole entropy from graviton entanglement,” arXiv:1211.0522
Original
Cited in the paper.

Then

M. Cvetič, G. W. Gibbons, D. Kubizňák, and C. N. Pope, “Black hole enthalpy and an entropy inequality for the thermodynamic volume,” Physical Review D
Original
2011
Later among the works it cites.
T.K. Finch, “The volume of the Schwarzschild black hole with respect to assorted time slicings,” (Nov., 2012), arXiv:1211.4337 [hep-th]
Original
2012
Later among the works it cites.

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