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  Existence of constant mean curvature foliations in spacetimes with two-dimensional local symmetry

Rendall, A. D. (1997). Existence of constant mean curvature foliations in spacetimes with two-dimensional local symmetry. Communications in Mathematical Physics, 189(1), 145-164. doi:10.1007/s002200050194.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-5A77-0 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-5A78-E
Genre: Journal Article

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331302.pdf (Publisher version), 174KB
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 Creators:
Rendall, Alan D.1, Author              
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1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:24012              

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 Abstract: It is shown that in a class of maximal globally hyperbolic spacetimes admitting two local Killing vectors, the past (defined with respect to an appropriate time orientation) of any compact constant mean curvature hypersurface can be covered by a foliation of compact constant mean curvature hypersurfaces. Moreover, the mean curvature of the leaves of this foliation takes on arbitrarily negative values and so the initial singularity in these spacetimes is a crushing singularity. The simplest examples occur when the spatial topology is that of a torus, with the standard global Killing vectors, but more exotic topologies are also covered. In the course of the proof it is shown that in this class of spacetimes a kind of positive mass theorem holds. The symmetry singles out a compact surface passing through any given point of spacetime and the Hawking mass of any such surface is non-negative. If the Hawking mass of any one of these surfaces is zero then the entire spacetime is flat.

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 Dates: 1997-10
 Publication Status: Published in print
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 Identifiers: eDoc: 331302
DOI: 10.1007/s002200050194
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Title: Communications in Mathematical Physics
  Alternative Title : Commun. Math. Phys.
Source Genre: Journal
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Pages: - Volume / Issue: 189 (1) Sequence Number: - Start / End Page: 145 - 164 Identifier: ISSN: 0010-3616
ISSN: 1432-0916