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ACTIONS FOR VACUUM EINSTEIN'S EQUATION WITH A KILLING SYMMETRY

HAN HE

Department of Physics, Beijing Normal University, Beijing 100875, China

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YONGGE MA

Department of Physics, Beijing Normal University, Beijing 100875, China

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, and

XUEJUN YANG

Department of Physics, Beijing Normal University, Beijing 100875, China

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https://doi.org/10.1142/S0218271803004274Cited by:1 (Source: Crossref)

Abstract

In a space–time M with a Killing vector field ξ^a which is either everywhere timelike or everywhere spacelike, the collection of all trajectories of ξ^a gives a three-dimensional space S. Besides the symmetry-reduced action from that of Einstein–Hilbert, an alternative action of the fields on S is also proposed which gives the same fields equations as those reduced from the vacuum Einstein equation on M.

Keywords:

PACS: 04.20.Fy, 04.20.Cv

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