Conserved Killing charges of quadratic curvature gravity theories in arbitrary backgrounds

TL;DR

This paper generalizes the Abbott-Deser-Tekin method to define conserved charges in quadratic curvature gravity theories across arbitrary backgrounds, enabling energy calculations for complex solutions like Lifshitz black holes.

Contribution

It introduces a new, background gauge invariant expression for conserved charges applicable to quadratic curvature gravity solutions with arbitrary asymptotes.

Findings

Derived a conserved charge formula valid for generic backgrounds.

Confirmed the formula reduces correctly to known cases.

Calculated energies for specific Lifshitz black hole solutions.

Abstract

We extend the Abbott-Deser-Tekin procedure of defining conserved quantities of asymptotically constant-curvature spacetimes, and give an analogous expression for the conserved charges of geometries that are solutions of quadratic curvature gravity models in generic D-dimensions and that have arbitrary asymptotes possessing at least one Killing isometry. We show that the resulting charge expression correctly reduces to its counterpart when the background is taken to be a space of constant curvature and, moreover, is background gauge invariant. As applications, we compute and comment on the energies of two specific examples: the three dimensional Lifshitz black hole and a five dimensional companion of the first, whose energy has never been calculated beforehand.