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

TL;DR

This paper introduces a new gauge-independent method to compute total energies and angular momenta in asymptotically anti-de Sitter spacetimes, extending the field theoretical approach to include a cosmological constant.

Contribution

It presents a novel prescription using a $(d-1)$-form for calculating conserved quantities in AdS spacetimes, applicable to higher dimensions and consistent with known results.

Findings

Successfully computes energies and angular momenta in 4D and 5D solutions

Method aligns with standard results for known solutions

Provides gauge-independent conserved quantities

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 $\Omega$ 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.