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arXiv:1411.2854gr-qc

How big is a black hole?

Marios Christodoulou, Carlo Rovelli

Early discovery. Linked by one identifiable commenter. This paper is outside the main ranking; a mention is not an endorsement.

Abstract

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.

arXiv comments
7 pages, 5 figures. References added
Journal reference
Phys. Rev. D 91, 064046 (2015)
DOI
doi:10.1103/PhysRevD.91.064046
Subjects
gr-qcGeneral Relativity and Quantum Cosmology

On Hacker News

Linked by 1 identifiable commenter in 5 comments across 5 threads, from Dec 2018 to May 2025.

Comments linking this paper, per year.

Discussed in comments5 threads

  1. Singularities in Space-Time Prove Hard to Kill 1 comment

    • The mean density of the interior is much much much lower than you think, because the Schwarzschild interior volume is enormously larger than that of a closed Euclidean 3-ball of the Schwarzschild radius. Some details: Christodoulou & Rovelli 2014 showed that the maximal interior…

      raattgiftView on HNParent context

  2. Thought experiments that fray the fabric of space-time 1 comment

    • The area of the Sun and the Earth and every other self-gravitating body in hydrostatic equilibrium is also proportional to the body's mass. Volumes are weird though: unlike area, relativistic volume can depend on the body's (and the spacetime's) history and composition rather…

      raattgiftView on HNParent context

  3. When a black hole and a neutron star merge 1 comment

    • >> any object can become a black hole if it is made dense enough [big 'if'!] > any material (of any density) can be made a black hole if there is enough of it There is an awful lot of intergalactic medium out there. It's of "any density" (albeit very low). How come it's not a…

      raattgiftView on HNParent context

  4. Are We Wrong About Black Holes? 1 comment

    • Unfortunately, Rovelli & Christodolou show [ https://arxiv.org/abs/1411.2854 ] that: independent of coordinate choice, the spatial 3-volume of a static Schwarzschild BH departs spectacularly from Euclidean geometry (not surprising); and in a collapsar asymptoting to…

      raattgiftView on HNParent context

  5. Why Black Hole Interiors Grow Almost Forever 1 comment

    • Neglecting evaporation, it's a lot closer to Yen Chin Ong's results (and those he cites, especially Christodoulou and Rovelli [2]) than most of the comments throughout this discussion, in that with a careful choice of time coordinate a spacelike spherical sector of a…

      raattgiftView on HNParent context

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