A covariant conservation theorem in general relativity

Physics

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Conservation Laws, Coordinate Transformations, Covariance, Gravitation Theory, Relativity, Einstein Equations, Gravitational Fields, Hamiltonian Functions, Integral Equations, Perturbation Theory

Scientific paper

The transformation of the Hamilton action integral of general relativity under infinitesimal coordinate transformations is used to derive a tensorial conservation theorem for the gravitational field. The total gravitational field is split into two parts: a 'background' field (assumed to be given) and a perturbative part. The resulting conservation theorem is exact, covariant, and of the Poynting type - i.e., only first derivatives of the perturbative field appear in it.

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