Geometric Inequality for Axisymmetric Black Holes With Angular Momentum
Fuente:
arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866912273906270208 |
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| author | Feng, Xuefeng Yan, Ruodi Gao, Sijie Lau, Yun-Kau Yau, Shing-Tung |
| author_facet | Feng, Xuefeng Yan, Ruodi Gao, Sijie Lau, Yun-Kau Yau, Shing-Tung |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_10590 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Geometric Inequality for Axisymmetric Black Holes With Angular Momentum Feng, Xuefeng Yan, Ruodi Gao, Sijie Lau, Yun-Kau Yau, Shing-Tung General Relativity and Quantum Cosmology 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. |
| title | Geometric Inequality for Axisymmetric Black Holes With Angular Momentum |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2312.10590 |