Vacuum Petrov type D horizons of non-trivial $U(1)$ bundle structure over Riemann surfaces with genus $>0$

Abstract

We consider isolated horizons (Killing horizons up to the second order) whose null flow has the structure of a U(1) principal fiber bundle over a compact Riemann surface. We impose the vacuum Einstein equations (with the cosmological constant) and the condition that the spacetime Weyl tensor is of Petrov D type on the geometry of the horizons. We derive all the solutions in the case when the genus of the surface is $>1$. By doing so for all the non-trivial bundles, we complete the classification. We construct the embedding spacetimes and show that they are locally isometric to the toroidal or hyperbolic generalization of the Taub-NUT-(anti-) de Sitter spacetimes for horizons of genus $1$ or $>1$ respectively, after performing Misner's identification of the spacetime. The horizon bundle structure can be naturally extended to bundle structure defined on the entire spacetime.

arXiv comment24 pages, minor typos corrected, version published in PRD

References in corpus (18)

• Isolated and dynamical horizons and their applications
• Stationary Black Holes: Uniqueness and Beyond
• Dynamical Horizons and their Properties
• Mechanics of Rotating Isolated Horizons
• Geometry of Generic Isolated Horizons
• Extremal Isolated Horizons: A Local Uniqueness Theorem
• Spacetimes foliated by Killing horizons
• Symmetric non-expanding horizons
• Horizons and Null Infinity: A Fugue in 4 voices
• Local version of the no-hair theorem
• The Petrov type D isolated null surfaces
• The axial symmetry of Kerr without the rigidity theorem
• The Petrov type D equation on genus $>0$ sections of isolated horizons
• Non-singular extension of the Kerr-NUT-(anti) de Sitter spacetimes
• Projectively non-singular horizons in Kerr-NUT-de Sitter spacetimes
• Non-singular Kerr-NUT-de Sitter spacetimes
• Extremal isolated horizons with $\Lambda$ and the related unique type D black holes
• Petrov type D equation on horizons of nontrivial bundle topology