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  Existence of maximal hypersurfaces in some spherically symmetric spacetimes

Burnett, G. A., & Rendall, A. D. (1996). Existence of maximal hypersurfaces in some spherically symmetric spacetimes. Classical and Quantum Gravity, 13(1), 111-123.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-5B6E-D Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-5B6F-B
Genre: Journal Article

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existence.pdf (Publisher version), 115KB
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 Creators:
Burnett, Gregory A., Author
Rendall, Alan D.1, Author              
Affiliations:
1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:24012              

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 Abstract: We prove that the maximal development of any spherically symmetric spacetime with collisionless matter (obeying the Vlasov equation) or a massless scalar field (obeying the massless wave equation) and possessing a constant mean curvature Cauchy surface also contains a maximal Cauchy surface. Combining this with previous results establishes that the spacetime can be foliated by constant mean curvature Cauchy surfaces with the mean curvature taking on all real values, thereby showing that these spacetimes satisfy the closed-universe recollapse conjecture. A key element of the proof, of interest in itself, is a bound for the volume of any Cauchy surface in any spacetime satisfying the timelike convergence condition in terms of the volume and mean curvature of a fixed Cauchy surface and the maximal distance between and . In particular, this shows that any globally hyperbolic spacetime having a finite lifetime and obeying the timelike-convergence condition cannot attain an arbitrarily large spatial volume.

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Language(s): eng - English
 Dates: 1996
 Publication Status: Published in print
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 Identifiers: eDoc: 330127
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Title: Classical and Quantum Gravity
  Alternative Title : Class. Quantum Grav.
Source Genre: Journal
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Pages: - Volume / Issue: 13 (1) Sequence Number: - Start / End Page: 111 - 123 Identifier: ISSN: 0264-9381