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Generalized Field Theoretical Approach to General Relativity and Conserved Quantities in Anti-de Sitter Spacetimes

N. Pinto-Neto·R. Rodrigues da Silva
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Abstract

A new prescription to calculate the total energies and angular momenta of asymptotically $(d+1)$-dimensional anti-de Sitter spacetimes is proposed. The method is based on an extension of the field theoretical approach to General Relativity to the case where there is an effective cosmological constant. A $(d-1)$-form $Ω$ is exhibited which, when integrated on asymptotic $(d-1)$-dimensional boundary surfaces, yields the values of those conserved quantities. The calculations are gauge independent once asymptotic conditions are not violated . Total energies and angular momenta of some known solutions in four and five dimensions are calculated agreeing with standard results.

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N. Pinto-Neto, R. Rodrigues da Silva. 2000-05-23. Generalized Field Theoretical Approach to General Relativity and Conserved Quantities in Anti-de Sitter Spacetimes. https://doi.org/10.1103/physrevd.61.104002

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