Mass of Rotating Black Holes in Gauged Supergravities

TL;DR

This paper calculates the masses of rotating black holes in gauged supergravities using the AMD and AD methods, confirming results with thermodynamics and addressing discrepancies caused by scalar fields.

Contribution

It demonstrates the effectiveness of the conformal AMD approach for mass calculation in gauged supergravities and compares it with the Abbott-Deser method, highlighting advantages and limitations.

Findings

AMD method yields consistent mass results with thermodynamics.

AD method agrees for minimal gauged supergravity but shows discrepancies otherwise.

Euclidean action calculation aligns with quantum statistical relations.

Abstract

The masses of several recently-constructed rotating black holes in gauged supergravities, including the general such solution in minimal gauged supergravity in five dimensions, have until now been calculated only by integrating the first law of thermodynamics. In some respects it is more satisfactory to have a calculation of the mass that is based directly upon the integration of a conserved quantity derived from a symmetry principal. In this paper, we evaluate the masses for the newly-discovered rotating black holes using the conformal definition of Ashtekar, Magnon and Das (AMD), and show that the results agree with the earlier thermodynamic calculations. We also consider the Abbott-Deser (AD) approach, and show that this yields an identical answer for the mass of the general rotating black hole in five-dimensional minimal gauged supergravity. In other cases we encounter discrepancies when applying the AD procedure. We attribute these to ambiguities or pathologies of the chosen decomposition into background AdS metric plus deviations when scalar fields are present. The AMD approach, involving no decomposition into background plus deviation, is not subject to such complications. Finally, we also calculate the Euclidean action for the five-dimensional solution in minimal gauged supergravity, showing that it is consistent with the quantum statistical relation.