Background-independent charges in Topologically Massive Gravity

TL;DR

This paper develops a background-independent method to define conserved charges in Topologically Massive Gravity, applicable to solutions with logarithmic terms and warped AdS black holes, enhancing the understanding of gravitational charges in complex spacetimes.

Contribution

It introduces a novel background-independent approach for calculating Noether charges in TMG, valid for solutions with logarithmic terms and warped geometries, without background subtraction.

Findings

Provides finite conserved charges for Log Gravity solutions.

Defines charges for warped AdS black holes without background subtraction.

Applicable at the chiral point with logarithmic terms.

Abstract

We construct background-independent Noether charges in Topologically Massive Gravity with negative cosmological constant using its first-order formulation. The procedure is carried out by keeping track of the surface terms in the variation of the action, regardless the value of the gravitational Chern-Simons coupling $\mu$. In particular, this method provides a definition of conserved quantities for solutions at the chiral point $\mu l = 1$ ($l$ is the AdS radius) that contain logarithmic terms (Log Gravity). It is also shown that the charge formula gives a finite result for warped AdS black holes without the need for any background-substraction procedure.