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arXiv · 2312.10590

Geometric Inequality for Axisymmetric Black Holes With Angular Momentum

Xuefeng Feng·Ruodi Yan·Sijie Gao·Yun-Kau Lau·Shing-Tung Yau
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Abstract

In an effort to understand the Penrose inequality for black holes with angular momentum, an axisymmetric, vacuum, asymptotically Euclidean initial data set subject to certain quasi-stationary conditions is considered for a case study. A new geometric definition of angular velocity of a rotating black hole is defined in terms of the momentum constraint, without any reference to a stationary Killing vector field. The momentum constraint is then shown to be equivalent to the dynamics of a two-dimensional steady compressible fluid flow governed by a quasi-conformal mapping. In terms of spinors, a generalised first law for rotating black holes (possibly with multi-connected horizon located along the symmetry axis) is then proven and may be regarded as a Penrose-type inequality for black holes with angular momentum.

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Xuefeng Feng, Ruodi Yan, Sijie Gao, Yun-Kau Lau, Shing-Tung Yau. 2023-12-17. Geometric Inequality for Axisymmetric Black Holes With Angular Momentum. https://arxiv.org/abs/2312.10590

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