Energy and Angular Momentum in Generic F(Riemann) Theories

TL;DR

This paper develops a method to compute conserved charges like energy and angular momentum in broad classes of gravity theories based on Riemann tensor contractions, extending previous approaches to more general theories.

Contribution

It introduces a generalized construction of conserved charges applicable to generic Riemann-based gravity theories in asymptotically (A)dS spacetimes, including explicit calculations for Born-Infeld gravity.

Findings

Derived explicit formulas for conserved charges in Riemann-based gravity theories.

Extended the ADT charge framework to more general gravitational actions.

Calculated energy and angular momentum of the BTZ black hole in Born-Infeld gravity.

Abstract

We construct the conserved charge of generic gravity theories built on arbitrary contractions of the Riemann tensor (but not on its derivatives) for asymptotically (anti)-de Sitter spacetimes. Our construction is a generalization of the ADT charges of linear and quadratic gravity theories in cosmological backgrounds. As an explicit example we find the energy and angular momentum of the BTZ black hole in the 2+1 dimensional Born-Infeld gravity.