Present status of the Penrose inequality

2009/06/30 by Marc Mars · 1 citation
Mathematics · Physics and Astronomy · #Cosmology and Gravitation Theories #Geometric Analysis and Curvature Flows #Noncommutative and Quantum Gravity Theories #gr-qc #math.DG

paper · pdf · doi:10.1088/0264-9381/26/19/193001

published as Class.Quant.Grav.26:193001,2009 · 54 pages, 3 figures, to be submitted as a Topical Review to Classical and Quantum Gravity

arxiv created 2009/06/30 · openalex publication_date 2009/09/22 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

The Penrose inequality gives a lower bound for the total mass of a spacetime in terms of the area of suitable surfaces that represent black holes. Its validity is supported by the cosmic censorship conjecture, and therefore its proof (or disproof) is an important problem in relation with gravitational collapse. The Penrose inequality is a very challenging problem in mathematical relativity and it has received continuous attention since its formulation by Penrose in the early seventies. Important breakthroughs have been made in the last decade or so, with the complete resolution of the so-called Riemannian Penrose inequality and a very interesting proposal to address the general case by Bray and Khuri. In this review, the most important results on this field will be discussed and the main ideas behind their proofs will be summarized, with the aim of presenting what is the status of our present knowledge in this topic.

Citations

• Positive Mass Theorem and the Boundary Behaviors of Compact Manifolds with Nonnegative Scalar Curvature
• Singularity Theorems and Their Consequences
• Asymptotic Behavior of Spherically Symmetric Marginally Trapped Tubes
• Gravitational waves in general relativity, VII. Waves from axi-symmetric isolated system
• Geometry of General Hypersurfaces in Spacetime: Junction Conditions
• Black holes in general relativity
• Gravitational waves in general relativity VIII. Waves in asymptotically flat space-time
• On the proof of the positive mass conjecture in general relativity
• From geometry to numerics: interdisciplinary aspects in mathematical and numerical relativity
• The mass of an asymptotically flat manifold
• Relativistic Equations for Adiabatic, Spherically Symmetric Gravitational Collapse
• The occurrence of singularities in cosmology. ɪɪɪ. Causality and singularities
• A new proof of the positive energy theorem
• Introduction to dynamical horizons in numerical relativity
• Über die physikalischen Grundlagen der Einsteinschen Gravitationstheorie
• On Continued Gravitational Contraction

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