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  Stationary solutions and asymptotic flatness I

Reiris, M. (2014). Stationary solutions and asymptotic flatness I. Classical and quantum gravity, 31(15): 155012. doi:10.1088/0264-9381/31/15/155012.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0023-CD0D-D Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0023-CD0E-B
Genre: Journal Article

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

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 Abstract: In general relativity, a stationary isolated system is defined as an asymptotically flat (AF) stationary spacetime with compact material sources. Other definitions that are less restrictive on the type of asymptotic could in principle be possible. Between this article and its sequel, we show that under basic assumptions, asymptotic flatness indeed follows as a consequence of Einsteinʼs theory. In particular, it is proved that any vacuum stationary spacetime-end whose (quotient) manifold is diffeomorphic to minus a ball and whose Killing field has its norm bounded away from zero, is necessarily AF with Schwarzschildian fall off. The 'excised' ball would contain (if any) the actual material body, but this information is unnecessary to reach the conclusion. In this first article, we work with weakly asymptotically flat (WAF) stationary ends, a notion that generalizes as much as possible that of the AF end, and prove that WAF ends are AF with Schwarzschildian fall off. Physical and mathematical implications are also discussed.

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 Dates: 2014
 Publication Status: Published in print
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 Identifiers: DOI: 10.1088/0264-9381/31/15/155012
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Title: Classical and quantum gravity
Source Genre: Journal
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Publ. Info: Bristol, U.K. : Institute of Physics
Pages: - Volume / Issue: 31 (15) Sequence Number: 155012 Start / End Page: - Identifier: ISSN: 0264-9381
CoNE: /journals/resource/954925513480_1