1994/11/21 by Markus Heusler, M. Heusler · 50 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Black hole (networking) #Charged black hole #Classical mechanics #Cosmology and Gravitation Theories #Energy condition #Event horizon #General relativity #Gravitational collapse #Horizon #Mathematical physics #Negative energy #Penrose process #Physics #Pulsars and Gravitational Waves Research #Quantum mechanics #Rotating black hole #Scalar field #Schwarzschild metric #Schwarzschild radius #Spacetime #White hole #gr-qc
paper · pdf · doi:10.1088/0264-9381/12/3/015
published in Classical and Quantum Gravity 12(3), 779-789 (IOP Publishing) · 16 pages, LATEX, no figures
arxiv created 1994/11/21 · openalex publication_date 1995/03/01 · arxiv updated 2010/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08
Requiring that the matter fields are subject to the dominant energy condition, we establish the lower bounds and for the total mass M of a static, spherically symmetric black hole spacetime. ( and denote the area and the surface gravity of the horizon, respectively.) Together with the fact that the Komar integral provides a simple relation between and the strong energy condition, this enables us to prove that the Schwarzschild metric represents the only static, spherically symmetric black hole solution of a self-gravitating matter model satisfying the dominant, but violating the strong energy condition for the timelike Killing field K at every point, that is . Applying this result to scalar fields, we recover the fact that the only black hole configuration of the spherically symmetric Einstein--Higgs model with arbitrary non-negative potential is the Schwarzschild spacetime with constant Higgs field. In the presence of electromagnetic fields, we also derive a stronger bound for the total mass, involving the electromagnetic potentials and charges. Again, this estimate provides a simple tool to prove a `no hair' theorem for matter fields violating the strong energy condition.