Local continuity laws on the phase space of Einstein equations with sources

Details Local continuity laws on the phase space of Einstein equations with sources Local continuity laws on the phase space of Einstein equations with sources

2002-04-16

arxiv.org/abs/gr-qc/0204054v1

Class. Quantum Grav. 18 (2001) 3629

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

LaTeX, 13 pages

Scientific paper

10.1088/0264-9381/18/17/315

Local continuity equations involving background fields and variantions of the fields, are obtained for a restricted class of solutions of the Einstein-Maxwell and Einstein-Weyl theories using a new approach based on the concept of the adjoint of a differential operator. Such covariant conservation laws are generated by means of decoupled equations and their adjoints in such a way that the corresponding covariantly conserved currents possess some gauge-invariant properties and are expressed in terms of Debye potentials. These continuity laws lead to both a covariant description of bilinear forms on the phase space and the existence of conserved quantities. Differences and similarities with other approaches and extensions of our results are discussed.

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