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Neutral and charged matter in equilibrium with black holes

K. A. Bronnikov^*

O. B. Zaslavskii^†

Center for Gravitation and Fundamental Metrology, VNIIMS, 46 Ozyornaya Street, Moscow 119361, Russia, and Institute of Gravitation and Cosmology, PFUR, 6 Miklukho-Maklaya Street, Moscow 117198, Russia

Department of Physics and Technology, Kharkov V.N. Karazin National University, 4 Svoboda Square, Kharkov, 61077, Ukraine

^*kb20@iyandex.ru
^†zaslav@ukr.net

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Phys. Rev. D 84, 084013 – Published 6 October, 2011

DOI: https://doi.org/10.1103/PhysRevD.84.084013

Abstract

We study the conditions of a possible static equilibrium between spherically symmetric, electrically charged or neutral black holes and ambient matter. The following kinds of matter are considered: (1) neutral and charged matter with a linear equation of state $p_{r} = w ρ$ (for neutral matter the results of our previous work are reproduced), (2) neutral and charged matter with $p_{r} \sim ρ^{m}$ , $m > 1$ , and (3) the possible presence of a “vacuum fluid” (the cosmological constant or, more generally, anything that satisfies the equality $T_{0}^{0} = T_{1}^{1}$ at least at the horizon). We find a number of new cases of such an equilibrium, including those generalizing the well-known Majumdar-Papapetrou conditions for charged dust. It turns out, in particular, that ultraextremal black holes cannot be in equilibrium with any matter in the absence of a vacuum fluid; meanwhile, matter with $w > 0$ , if it is properly charged, can surround an extremal charged black hole.

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References (15)

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Neutral and charged matter in equilibrium with black holes

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