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

R. Cartas-Fuentevilla
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Abstract

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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R. Cartas-Fuentevilla. 2002-04-16. Local continuity laws on the phase space of Einstein equations with sources. https://doi.org/10.1088/0264-9381%2F18%2F17%2F315

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