Uniqueness of the Kerr-de Sitter spacetime as an algebraically special\n solution in five dimensions

2015/01/12 by Gabriel Bernardi de Freitas, de Freitas, Gabriel Bernardi, Mahdi Godazgar +3 · 2 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Relativity and Gravitational Theory

paper · pdf · doi:10.48550/arxiv.1501.02837

Abstract

We determine the most general solution of the five-dimensional vacuum\nEinstein equation, allowing for a cosmological constant, with (i) a Weyl tensor\nthat is type II or more special in the classification of Coley et al., (ii) a\nnon-degenerate "optical matrix" encoding the expansion, rotation and shear of\nthe aligned null direction. The solution is specified by three parameters. It\nis locally isometric to the 5d Kerr-de Sitter solution, or related to this\nsolution by analytic continuation or taking a limit. This is in contrast with\nfour dimensions, where there exist infinitely many solutions with properties\n(i) and (ii).\n

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