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Actions for Vacuum Einstein's Equation with a Killing Symmetry

Han He·Yongge Ma·Xuejun Yang
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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 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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Han He, Yongge Ma, Xuejun Yang. 2003-04-01. Actions for Vacuum Einstein's Equation with a Killing Symmetry. https://doi.org/10.1142/s0218271803004274

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