2010/05/07 by William Ballik, Ballik, William, Kayll Lake +1 · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Astrophysical Phenomena (astro-ph.HE) #High Energy Physics - Theory (hep-th) #Relativity and Gravitational Theory #astro-ph.HE #gr-qc #hep-th
paper · pdf · doi:10.48550/arxiv.1005.1116
revtex4, 6 pages, 12 figures. Much expanded discussion
openalex publication_date 2010/05/07 · arxiv created 2010/06/01 · arxiv updated 2010/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The invariant four-volume V of a complete black hole (the volume of the spacetime at and interior to the horizon) diverges. However, if one considers the black hole set up by the gravitational collapse of an object, and integrates only a finite time to the future of the collapse, the resultant volume is well defined and finite. In this paper we examine non-degenerate stationary black holes (and cosmological horizons) and find that Vs \varpropto ln(λ) where s is any shell that terminates on the horizon, λ is the affine generator of the horizon and the constant of proportionality is the Parikh volume of s divided by the surface gravity. This provides an alternative local and invariant definition of the surface gravity of a stationary black hole.