1993/05/25 by Robert M. Wald, Wald, Robert M. · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Black hole (networking) #Black hole thermodynamics #Charged black hole #Classical mechanics #Cosmology and Gravitation Theories #Entropy (arrow of time) #Extremal black hole #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical analysis #Mathematical physics #Mathematics #Nonsingular black hole models #Physics #Quantum mechanics #Relativity and Gravitational Theory #Theoretical physics #Uniqueness #gr-qc
paper · pdf · doi:10.48550/arxiv.gr-qc/9305022
9 pages, to appear in Misner Festschrift
arxiv created 1993/05/25 · openalex publication_date 1993/05/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A simple proof of a strengthened form of the first law of black hole mechanics is presented. The proof is based directly upon the Hamiltonian formulation of general relativity, and it shows that the the first law variational formula holds for arbitrary nonsingular, asymptotically flat perturbations of a stationary, axisymmetric black hole, not merely for perturbations to other stationary, axisymmetric black holes. As an application of this strengthened form of the first law, we prove that there cannot exist Einstein-Maxwell black holes whose ergoregion is disjoint from the horizon. This closes a gap in the black hole uniqueness theorems.