Actions for Vacuum Einstein's Equation with a Killing Symmetry

Details Actions for Vacuum Einstein's Equation with a Killing Symmetry Actions for Vacuum Einstein's Equation with a Killing Symmetry

2002-12-25

arxiv.org/abs/gr-qc/0212101v2

Int.J.Mod.Phys. D12 (2003) 1961

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

8 pages, the difference between the action we proposed and the symmetry-reduced action is clarified

Scientific paper

10.1142/S0218271803004274

In a space-time $M$ with a Killing vector field $\xi^a$ which is either everywhere timelike or everywhere spacelike, the collection of all trajectories of $\xi^a$ gives a 3-dimension 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 $M$.

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