Effective action for the field equations of charged black holes

TL;DR

This paper derives a general effective action for charged black holes in N=2 supergravity, extending BPS techniques to multi-centered, non-supersymmetric solutions, and connects it to the entropy function framework.

Contribution

It provides a new, general form of the black hole potential and explicit constraints for multi-centered, non-supersymmetric black hole solutions in supergravity.

Findings

Derived a generalized effective action for non-supersymmetric black holes.

Explicitly calculated additional solution constraints.

Linked the effective action to the entropy function for spherically symmetric cases.

Abstract

In this article, we consistently reduce the equations of motion for the bosonic N = 2 supergravity action, using a multi-centered black hole ansatz for the metric. This reduction is done in a general, non-supersymmetric setup, in which we extend concepts of BPS black hole technology. First of all we obtain a more general form of the black hole potential, as part of an effective action for both the scalars and the vectors in the supergravity theory. Furthermore, we show that there are extra constraints specifying the solution, which we calculate explicitly. In the literature, these constraints have already been studied in the one-center case. We also show that the effective action we obtain for non-static metrics, can be linked to the "entropy function" for the spherically symmetric case, as defined by Sen and Cardoso et al.