Accelerating Black Holes and Spinning Spindles

TL;DR

This paper constructs and analyzes accelerating, rotating, charged black hole solutions in AdS4, uplifts them to 11D supergravity to eliminate singularities, and explores their supersymmetric limits and dual gauge theory interpretations.

Contribution

It introduces a method to remove conical singularities in accelerating black holes by uplift to 11D supergravity and studies their supersymmetric and extremal limits.

Findings

Uplifted solutions eliminate conical singularities.

New supersymmetric AdS2 x Y9 solutions with rotation.

Black hole entropy linked to dual gauge theories.

Abstract

We study solutions in the Pleba\'nski--Demia\'nski family which describe an accelerating, rotating and dyonically charged black hole in $AdS_4$. These are solutions of $D=4$ Einstein-Maxwell theory with a negative cosmological constant and hence minimal $D=4$ gauged supergravity. It is well known that when the acceleration is non-vanishing the $D=4$ black hole metrics have conical singularities. By uplifting the solutions to $D=11$ supergravity using a regular Sasaki-Einstein $7$-manifold, $SE_7$, we show how the free parameters can be chosen to eliminate the conical singularities. Topologically, the $D=11$ solutions incorporate an $SE_7$ fibration over a two-dimensional weighted projective space, $\mathbb{WCP}^1_{[n_-,n_+]}$, also known as a spindle, which is labelled by two integers that determine the conical singularities of the $D=4$ metrics. We also discuss the supersymmetric and extremal limit and show that the near horizon limit gives rise to a new family of regular supersymmetric $AdS_2\times Y_9$ solutions of $D=11$ supergravity, which generalise a known family by the addition of a rotation parameter. We calculate the entropy of these black holes and argue that it should be possible to derive this from certain ${\cal N}=2$, $d=3$ quiver gauge theories compactified on a spinning spindle with appropriate magnetic flux.