Generalized field theoretical approach to general relativity and conserved quantities in anti–de Sitter spacetimes

A new prescription to calculate the total energies and angular momenta of asymptotically $\mathrm{}(d+1\mathrm{})\mathrm{}$-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 $\left(d-1\right)$ form $\Omega$ is exhibited which, when integrated on asymptotic $\left(d-1\right)$-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.