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