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  Perturbative Solutions of the Extended Constraint Equations in General Relativity

Butscher, A. (2007). Perturbative Solutions of the Extended Constraint Equations in General Relativity. Communications in Mathematical Physics, 272(1), 1-23. doi:10.1007/s00220-007-0204-8.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-4851-4 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-4852-2
Genre: Journal Article

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 Creators:
Butscher, Adrian1, 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: The extended constraint equations arise as a special case of the conformal constraint equations that are satisfied by an initial data hypersurface $Z$ in an asymptotically simple spacetime satisfying the vacuum conformal Einstein equations developed by H. Friedrich. The extended constraint equations consist of a quasi-linear system of partial differential equations for the induced metric, the second fundamental form and two other tensorial quantities defined on $Z$, and are equivalent to the usual constraint equations that $Z$ satisfies as a spacelike hypersurface in a spacetime satisfying Einstein's vacuum equation. This article develops a method for finding perturbative, asymptotically flat solutions of the extended constraint equations in a neighbourhood of the flat solution on Euclidean space. This method is fundamentally different from the `classical' method of Lichnerowicz and York that is used to solve the usual constraint equations.

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Language(s): eng - English
 Dates: 2007-05
 Publication Status: Published in print
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 Identifiers: eDoc: 23721
Other: arXiv:gr-qc/0211037
DOI: 10.1007/s00220-007-0204-8
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Title: Communications in Mathematical Physics
Source Genre: Journal
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Pages: - Volume / Issue: 272 (1) Sequence Number: - Start / End Page: 1 - 23 Identifier: -