Gravitational energy-momentum on nonmaximal surfaces

Abstract

Gravitational Cauchy data defined iteratively from an input set which is of pure linearized gauge form representing a nonflat hypersurface appear to possess tachyonic energy-momentum P^μ. We show that such systems do behave correctly: P^μ is positive timelike, and vanishing of the energy implies flat space. Although the P^μ begin at quartic order in the inputs, it is possible to exhibit explicitly the helicity-2 character of the gravitational excitations on which both the energy and the flatness conditions depend.

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