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  Static solutions from the point of view of comparison geometry

Reiris, M. (2012). Static solutions from the point of view of comparison geometry. Journal of Mathematical Physics, 53: 012501. doi:10.1063/1.3668045.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0028-FE58-4 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0028-FE59-2
Genre: Journal Article

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 Creators:
Reiris, Martin1, Author              
Affiliations:
1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24012              

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Free keywords: General Relativity and Quantum Cosmology, gr-qc,Mathematics, Differential Geometry, math.DG
 Abstract: We analyze (the harmonic map representation of) static solutions of the Einstein Equations in dimension three from the point of view of comparison geometry. We find simple monotonic quantities capturing sharply the influence of the Lapse function on the focussing of geodesics. This allows, in particular, a sharp estimation of the Laplacian of the distance function to a given (hyper)-surface. We apply the technique to asymptotically flat solutions with regular and connected horizons and, after a detailed analysis of the distance function to the horizon, we recover the Penrose inequality and the uniqueness of the Schwarzschild solution. The proof of this last result does not require proving conformal flatness at any intermediate step.

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 Dates: 2011-03-242012
 Publication Status: Published in print
 Pages: 41 pages
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1103.4765
DOI: 10.1063/1.3668045
URI: http://arxiv.org/abs/1103.4765
 Degree: -

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Title: Journal of Mathematical Physics
Source Genre: Journal
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Publ. Info: Woodbury, N.Y. [etc.] : American Institute of Physics
Pages: - Volume / Issue: 53 Sequence Number: 012501 Start / End Page: - Identifier: ISSN: 0022-2488
CoNE: /journals/resource/954922836227