2008/01/31 by К. А. Бронников, K. A. Bronnikov, O. B. Zaslavskii +1 · 29 citations
Physics and Astronomy · #Astrophysics #Black Holes and Theoretical Physics #Black hole (networking) #Cosmology and Gravitation Theories #Horizon #Integer (computer science) #Isotropy #Mathematical physics #Perfect fluid #Physics #Quantum mechanics #Relativity and Gravitational Theory #Star (game theory) #astro-ph #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.78.021501
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 78(2) (American Physical Society) · 5 pages, no figures. Some discussion added, misprints corrected
arxiv created 2008/05/29 · openalex publication_date 2008/07/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study equilibrium conditions between a static, spherically symmetric black hole and classical matter in terms of the radial pressure to density ratio pr/\ensuremathρ=w(u), where u is the radial coordinate. It is shown that such an equilibrium is possible in two cases: (i) the well-known case w\ensuremath→\ensuremath-1 as u\ensuremath→uh (the horizon), i.e., ``vacuum'' matter, for which \ensuremathρ(uh) can be nonzero; (ii) w\ensuremath→\ensuremath-1/(1+2k) and \ensuremathρ\ensuremath∼(u\ensuremath-uh)k as u\ensuremath→uh, where k>0 is a positive integer (w=\ensuremath-1/3 in the generic case k=1). A noninteracting mixture of these two kinds of matter can also exist. The whole reasoning is local, hence the results do not depend on any global or asymptotic conditions. They mean, in particular, that a static black hole cannot live inside a star with nonnegative pressure and density. As an example, an exact solution for an isotropic fluid with w=\ensuremath-1/3 (that is, a fluid of disordered cosmic strings), with or without vacuum matter, is presented.