paper

Kerr-de Sitter Universe

arXiv:1011.0479 · doi:10.1088/0264-9381/28/8/085012

Abstract

It is now widely accepted that the universe as we understand it is accelerating in expansion and fits the de Sitter model rather well. As such, a realistic assumption of black holes must place them on a de Sitter background and not Minkowski as is typically done in General Relativity. The most astrophysically relevant black hole is the uncharged, rotating Kerr solution, a member of the more general Kerr-Newman metrics. A generalization of the rotating Kerr black hole to a solution of the Einstein's equation with a cosmological constant was discovered by Carter \cite{DWDW}. It is typically referred to as the Kerr-de Sitter spacetime. Here, we discuss the horizon structure of this spacetime and its dependence on . We recall that in a $\La>0$ universe, the term `extremal black hole' refers to a black hole with angular momentum . We obtain explicit numerical results for the black hole's maximal spin value and get a distribution of admissible Kerr holes in the (, spin) parameter space. We look at the conformal structure of the extended spacetime and the embedding of the 3-geometry of the spatial hypersurfaces. In analogy with Reissner-Nordström -de Sitter spacetime, in particular by considering the Kerr-de Sitter causal structure as a distortion of the Reissner-Nordström-de Sitter one, we show that spatial sections of the extended spacetime are 3-spheres containing 2-dimensional topologically spherical sections of the horizons of Kerr holes at the poles. Depending on how a constant 3-space is defined these holes may be seen as black or white holes (four possible combinations).

20 pages, 9 figures

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