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arXiv · 2403.19383

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

Jerzy Lewandowski·Maciej Ossowski
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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.

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Jerzy Lewandowski, Maciej Ossowski. 2024-03-28. Vacuum Petrov type D horizons of non-trivial $U(1)$ bundle structure over Riemann surfaces with genus $> 0$. https://doi.org/10.1103/physrevd.110.024071

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