Quasi-Local Conserved Charges in Covariant Theory of Gravity

TL;DR

This paper develops a covariant, Lagrangian-based method to define quasi-local conserved charges in higher derivative gravity theories, enabling better analysis of black hole properties and asymptotic behaviors.

Contribution

It introduces a covariant formulation linking linearized and non-linear conserved currents, providing a new prescription for quasi-local charges in higher derivative gravity.

Findings

Demonstrates angular momentum invariance in black holes

Reproduces linearized potential in asymptotic AdS space

Provides a covariant, Lagrangian-based charge definition

Abstract

In any generally covariant theory of gravity, we show the relationship between the linearized asymptotically conserved current and its non-linear completion through the identically conserved current. Our formulation for conserved charges is based on the Lagrangian description, and so completely covariant. By using this result, we give a prescription to define quasi-local conserved charges in any higher derivative gravity. As applications of our approach, we demonstrate the angular momentum invariance along the radial direction of black holes and reproduce more efficiently the linearized potential on the asymptotic AdS space.