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Conserved Killing charges of quadratic curvature gravity theories in arbitrary backgrounds

Devecioglu, Deniz Olgu
Sarıoğlu, Bahtiyar Özgür
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 before.