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Journal of Mathematical Physics / Volume 53 / Issue 2 / ARTICLES / General Relativity and Gravitation

J. Math. Phys. 53, 022502 (2012); http://dx.doi.org/10.1063/1.3682242 (10 pages)

Spacelike hypersurfaces with negative total energy in de Sitter spacetime

Zhuobin Liang and Xiao Zhang

Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People's Republic of China

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(Received 18 August 2011; accepted 14 January 2012; published online 3 February 2012)

De Sitter spacetime can be separated into two parts along two kinds of hypersurfaces and the half-de Sitter spacetimes are covered by the planar and hyperbolic coordinates, respectively. Two positive energy theorems were proved previously for certain P-asymptotically de Sitter and H-asymptotically de Sitter initial data sets by the second author and collaborators. These initial data sets are asymptotic to time slices of the two kinds of half-de Sitter spacetimes, respectively, and their mean curvatures are bounded from above by certain constants. While the mean curvatures violate these conditions, the spacelike hypersurfaces with negative total energy in the two kinds of half-de Sitter spacetimes are constructed in this short paper.

© 2012 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. POSITIVE ENERGY THEOREMS
  3. NEGATIVE TOTAL ENERGY

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KEYWORDS and PACS

Keywords

space-time configurations

PACS

  • 04.20.Gz

    Spacetime topology, causal structure, spinor structure

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3682242

PUBLICATION DATA

ISSN

0022-2488 (print)  
1089-7658 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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