Local version of the no-hair theorem

Abstract

Non-extremal isolated horizons embeddable in 4-dimensional spacetimes satisfying the vacuum Einstein equations with cosmological constant are studied. The horizons are assumed to be stationary to the second order. The Weyl tensor at the horizon is assumed to be of the Petrov type D. The corresponding equation on the intrinsic horizon geometry is solved in the axisymmetric case. The family of the solutions is $2$-dimensional, it is parametrized by the area and the angular momentum. The embeddability in the Kerr - de Sitter, the Kerr - anti de Sitter and the Near extremal Horizon spacetimes obtained by the Horowitz limit from the extremal Kerr - de Sitter and extremal Kerr - anti de Sitter is discussed. This uniqueness of the axisymmetric type D isolated horizons is a generalization of the similar earlier result valid in the cosmological constant free case.

RevTex4-1, BibTex, 19 pages

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Cited by in corpus (11)

• The Petrov type D isolated null surfaces
• The Petrov type D equation on genus $>0$ sections of isolated horizons
• Killing spinor data on distorted black hole horizons and the uniqueness of stationary vacuum black holes
• Non-singular extension of the Kerr-NUT-(anti) de Sitter spacetimes
• Non-singular Kerr-NUT-de Sitter spacetimes
• Axisymmetric, extremal horizons in the presence of a cosmological constant
• Projectively non-singular horizons in Kerr-NUT-de Sitter spacetimes
• Petrov type D equation on horizons of nontrivial bundle topology
• Spacetime near Kerr isolated horizon
• Isolated horizons of the Hopf bundle structure transversal to the null direction, the horizon equations and embeddability in NUT-like spacetimes
• Vacuum Petrov type D horizons of non-trivial $U(1)$ bundle structure over Riemann surfaces with genus $>0$