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arXiv · 1904.12167

A complete classification of S1-symmetric static vacuum black holes

Martín Reiris·Javier Peraza
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Abstract

In a seminal paper of 1917, H. Weyl presented a remarkable reduction of the static axisymmetric vacuum Einstein equations, serving as a relatively straightforward technique to generate and explore new solutions. Weyl's reduction was used by Myers in 1987, and independently by Korotkin-Nicolai in 1994, to construct a new family of static and axisymmetric solutions with compact non-empty horizon, however with non-trivial topology and asymptotically Kasner. This family, together with the Schwarzschild and the Boost families, remained until now as the only known S1-symmetric static black hole solutions, namely, (metrically complete) S1-symmetric static vacuum solutions with compact and non-empty horizon. In this article we prove that, indeed, these three families exhaust all the examples of S1-symmetric static vacuum black holes.

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Martín Reiris, Javier Peraza. 2019-04-27. A complete classification of S1-symmetric static vacuum black holes. https://doi.org/10.1088/1361-6382%2Fab497c

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