Background-independent charges in Topologically Massive Gravity

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.