Spherical Black Holes in Cosmological and Other Fluid Backgrounds: An Overview

Malcolm Anderson
(Universiti Brunei Darusslam)


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A longstanding problem in classical general relativity concerns the embedding of a non-rotating (spherical) black hole in a cosmological background. It is well known that the only static solutions of the Einstein equations describing a spherical black hole in a cosmological background are the Schwarzschild-de Sitter and Schwarzschild-anti-de Sitter metrics. But there exists in addition a large class of non-static solutions, which includes the McVittie [1] and generalised McVittie [2] metrics, the Sultana-Dyer solution [3], a family of self-similar metrics due to Saida, Harada, Maeda and Nozawa [4, 5], and the Clifton solutions [6].

In this talk I will review the history of the problem of what are often called “dynamical black holes”, and discuss in particular a recent dispute between Bachichev at al. [7] and Gao et al. [8] over the claim that the mass of a black hole can be reduced as a result of the accretion of phantom energy (that is, a fluid with p/rho <-1).

[1] McVittie GC (1933), Mon. Not. R. Astr. Soc. 93, 325.
[2] Faraoni V and Jacques A (2007), Phys. Rev. D76, 063510.
[3] Sultana J and Dyer CC (2005), Gen. Rel. Grav. 37, 1349.
[4] Saida H, Harada T and Maeda H (2007), Class. Quant. Grav. 24, 4711.
[5] Nozawa M and Maeda H (2008), Class. Quant. Grav. 25, 055009.
[6] Clifton T (2006), Class. Quant. Grav. 23, 7445.
[7] Babichev E, Dokuchaev V and Eroshenko Yu (2004), Phys. Rev. Lett. 93, 021102.
[8] Gao C, Chen X, Faraoni V and Shen Y-G (2008), Class. Quant. Grav. D78, 024008.