Nonstationary energy in general relativity

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2020-01-15
Altas, Emel
Tekin, Bayram
Using the time evolution equations of (cosmological) general relativity in the first order Fischer-Marsden form, we construct an integral that measures the amount of nonstationary energy on a given spacelike hypersurface in D dimensions. The integral vanishes for stationary spacetimes; and with a further assumption, reduces to Dain's invariant on the boundary of the hypersurface which is defined with the Einstein constraints and a fourth order equation defining approximate Killing symmetries.