The 2m ≤ r property of spherically symmetric static space-times

1996/08/01 by Marc Mars, M. M. Martin-Prats, M Mercè Martín-Prats +2 · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Computer science #Cosmology and Gravitation Theories #Energy (signal processing) #Isotropy #Matching (statistics) #Mathematical analysis #Mathematical physics #Mathematics #Perfect fluid #Physics #Property (philosophy) #Pure mathematics #Quantum mechanics #Relativity and Gravitational Theory #Space (punctuation) #Symmetric space #gr-qc

paper · pdf · doi:10.1016/0375-9601(96)00391-x

published as Phys.Lett. A218 (1996) 147-150 · Latex, no figures

openalex publication_date 1996/08/01 · arxiv created 2002/02/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We prove that all spherically symmetric static spacetimes which are both regular at r=0 and satisfying the single energy condition rho + p_r + p_t >= 0 cannot contain any black hole region (equivalently, they must satisfy 2m/r <= 1 everywhere). This result holds even when the spacetime is allowed to contain a finite number of matching hypersurfaces. This theorem generalizes a result by Baumgarte and Rendall when the matter contents of the space-time is a perfect fluid and also complements their results in the general non-isotropic case.

Citations

• Geometry of General Hypersurfaces in Spacetime: Junction Conditions
• The Large Scale Structure of Space-Time

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