2002/01/31 by Edward Malec, Marc Mars, Walter Simon · 1 citation
Mathematics · Physics and Astronomy · #Apparent horizon #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Curvature #Einstein #Event horizon #Geometric Analysis and Curvature Flows #Geometry #Inverse #Mathematical analysis #Mathematical physics #Mathematics #Minimal surface #Monotonic function #Physics #Quantum mechanics #Scalar (mathematics) #Scalar curvature #Smoothness #Spacetime #Theoretical physics #gr-qc #hep-th #math.DG
paper · pdf · doi:10.1103/physrevlett.88.121102
published as Phys.Rev.Lett. 88 (2002) 121102 · 4 pages, revtex, no figures. Some comments added. No essential changes. To be published in Phys. Rev. Lett
arxiv created 2002/02/13 · openalex publication_date 2002/03/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
For asymptotically flat initial data of Einstein's equations satisfying an energy condition, we show that the Penrose inequality holds between the Arnowitt-Deser-Misner mass and the area of an outermost apparent horizon, if the data are suitably restricted. We prove this by generalizing Geroch's proof of monotonicity of the Hawking mass under a smooth inverse mean curvature flow, for data with non-negative Ricci scalar. Unlike Geroch we need not confine ourselves to minimal surfaces as horizons. Leaving smoothness issues aside, we also show that our restrictions on the data can be locally fulfilled by a suitable choice of the initial surface in a given spacetime.