The Kerrde Sitter universe

Sarp Akcay (1, 2) , Richard A Matzner (3, 4)

1 University of Southampton
2 University of Texas at Austin [Austin]
3 Center for Relativity
4 Texas Cosmology Center

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 Λ was discovered by Carter [ 1 ]. It is typically referred to as the Kerr-de Sitter spacetime. Here, we discuss the horizon structure of this spacetime and its dependence on Λ. We recall that in a Λ > 0 universe, the term 'extremal black hole ' refers to a black hole with angular momentum J > M 2. We obtain explicit numerical results for the black hole's maximal spin value and get a distribution of admissible Kerr holes in the (Λ, 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 t = constant 3-space is defined these holes may be seen as black or white holes (four possible combinations).

Mots clés: Physical Sciences

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]

Sarp Akcay, Richard A Matzner. The Kerrde Sitter universe. Classical and Quantum Gravity, 2011, 28 (8), pp.85012. ⟨10.1088/0264-9381/28/8/085012⟩. ⟨hal-00690082⟩