Multi-centered black holes in gauged D=5 supergravity

TL;DR

This paper constructs a family of time-dependent multi-center black hole solutions in D=5, N=2 gauged supergravity, offering a partial step toward understanding multi-center configurations in curved AdS backgrounds.

Contribution

It introduces a novel family of complex, time-dependent multi-center black hole solutions in gauged supergravity, extending previous ungauged results to curved backgrounds.

Findings

Solutions are complex and not fully physical but suggest possible Wick rotation interpretations.

Generalizable to AdS supergravities in various dimensions.

Provides a partial realization of multi-center black holes in gauged supergravity.

Abstract

One of the important consequences of the no-force condition for BPS states is the existence of stable static multi-center solutions, at least in ungauged supergravities. This observation has been at the heart of many developments in brane physics, including the construction of intersecting branes and reduced symmetry D-brane configurations corresponding to the Coulomb branch of the gauge theory. However the search for multi-center solutions to gauged supergravities has proven rather elusive. Because of the background curvature, it appears such solutions cannot be static. Nevertheless even allowing for time dependence, general multi-center solutions to gauged supergravity have yet to be constructed. In this letter we investigate the construction of such solutions for the case of D=5, N=2 gauged supergravity coupled to an arbitrary number of vector multiplets. Formally, we find a family of time dependent multi-center black hole solutions which are easily generalized to the case of AdS supergravities in general dimensions. While these are not true solutions, as they have a complex metric and gauge potential, they may be related to a Wick rotated theory or to a theory where the coupling is taken to be imaginary. These solutions thus provide a partial realization of true multi-center black-holes in gauged supergravities.