Nonuniqueness of capped black holes: large and small bubbles

TL;DR

This paper introduces a new class of five-dimensional black hole solutions with non-trivial topology, revealing non-uniqueness and different entropy properties among solutions with identical conserved charges.

Contribution

It constructs a four-parameter, non-BPS, asymptotically flat black hole solution with non-trivial topology, extending previous solutions and demonstrating non-uniqueness in capped black holes.

Findings

Two distinct solution branches: small and large bubbles.

Solutions are free of singularities and closed timelike curves.

Large/small bubbles can have higher/lower entropy than known black holes.

Abstract

We present a new non-BPS solution describing an asymptotically flat, stationary, bi-axisymmetric capped black hole in the bosonic sector of five-dimensional minimal supergravity. This solution describes a spherical black hole, while the exterior region of the horizon exhibits a non-trivial topology of $[{\mathbb R}^4 \# {\mathbb C}{\mathbb P}^2] \setminus {\mathbb B}^4$ on a timeslice. This solution extends our previously constructed three-parameter solution to a more general four-parameter solution. To derive this solution, we utilize a combination of the Ehlers and Harrison transformations and then impose appropriate boundary conditions on the solution's parameters. It can be shown that the resultant solution is free from curvature, conical, Dirac-Misner string and orbifold singularities, as well as closed timelike curves on and outside the horizon. Characterized by four independent conserved charges -- mass, two angular momenta, and electric charge -- this solution reveals two distinct branches: a small bubble branch and a large bubble branch, distinguished by non-conserved local quantities such as magnetic flux or magnetic potential. This shows the non-uniqueness for spherical black holes, even among capped black holes. For equivalent sets of conserved charges, we find that the large/small bubble branch can have larger/smaller entropy than the Cveti\v{c}-Youm black hole.