A toy Penrose inequality and its proof

We formulate and prove a toy version of the Penrose inequality. The formulation mimics the original Penrose inequality in which the scenario is the following: a shell of null dust collapses in Minkowski space and a marginally trapped surface forms on it. Through a series of arguments relying on esta...

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Bibliographic Details
Published inGeneral relativity and gravitation Vol. 48; no. 12; pp. 1 - 12
Main Authors Bengtsson, Ingemar, Jakobsson, Emma
Format Journal Article
LanguageEnglish
Published New York Springer US 01.12.2016
Springer Nature B.V
Subjects
Anti-de Sitter space
Astronomy
Astrophysics and Cosmology
Black holes
Classical and Quantum Gravitation
Differential Geometry
Editor's Choice (Research Article)
Gravity
Inequality
Mathematical and Computational Physics
Minkowski space
Penrose inequality
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
teoretisk fysik
Theoretical
Theoretical Physics
Penrose inequality
Black holes
Anti-de Sitter space
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Summary:We formulate and prove a toy version of the Penrose inequality. The formulation mimics the original Penrose inequality in which the scenario is the following: a shell of null dust collapses in Minkowski space and a marginally trapped surface forms on it. Through a series of arguments relying on established assumptions, an inequality relating the area of this surface to the total energy of the shell is formulated. Then a further reformulation turns the inequality into a statement relating the area and the outer null expansion of a class of surfaces in Minkowski space itself. The inequality has been proven to hold true in many special cases, but there is no proof in general. In the toy version here presented, an analogous inequality in (2  +  1)-dimensional anti-de Sitter space turns out to hold true.
ISSN:0001-7701
1572-9532
1572-9532
DOI:10.1007/s10714-016-2155-x