Geometric inequalities in spherically symmetric spacetimes

In geometric inequalities ADM mass plays more fundamental role than the concept of quasi-local mass. This paper is to demonstrate that using the quasi-local mass some new insights can be acquired. In spherically symmetric spacetimes the Misner–Sharp mass and the concept of the Kodama vector field pr...

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Bibliographic Details
Published in:General relativity and gravitation 2017-07, Vol.49 (7), p.1-12, Article 94
Main Author: Csukás, Károly Z.
Format: Article
Language:English
Subjects:
Astronomy
Astrophysics and Cosmology
Classical and Quantum Gravitation
Differential Geometry
Gravity
Inequalities
Mathematical and Computational Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Research Article
Spacetime
Symmetry
Theoretical
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Summary:In geometric inequalities ADM mass plays more fundamental role than the concept of quasi-local mass. This paper is to demonstrate that using the quasi-local mass some new insights can be acquired. In spherically symmetric spacetimes the Misner–Sharp mass and the concept of the Kodama vector field provides an ideal setting to the investigations of geometric inequalities. We applying the proposed new techniques to investigate the spacetimes containing black hole or cosmological horizons but we shall also apply them in context of normal bodies. Most of the previous investigations applied only the quasi-local charges and the area. Our main point is to include the quasi-local mass in the corresponding geometrical inequalities. This way we recover some known relations but new inequalities are also derived.
ISSN:0001-7701
1572-9532
DOI:10.1007/s10714-017-2256-1