Geometric inequality for axisymmetric black holes with angular momentum

• Published in: Classical and quantum gravity Vol. 42; no. 6; pp. 65022 - 65040
• Main Authors: Feng, Xuefeng, Yan, Ruodi, Gao, Sijie, Lau, Yun-Kau, Yau, Shing-Tung
• Format: Journal Article
• Language: English
• Published: IOP Publishing 21.03.2025
• Subjects: geometric inequality; momentum constraint; rotating black holes
• ISSN: 0264-9381; 1361-6382
• DOI: 10.1088/1361-6382/adb82a

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.