Black Rings in Supergravity

TL;DR

This paper constructs explicit five-dimensional black ring solutions in supergravity with multiple charges and angular momentum, analyzing their thermodynamic properties and including solutions with background magnetic fields.

Contribution

It provides the first explicit supergravity solutions for black rings with three dipole and three electric charges, and studies their thermodynamics and singularity conditions.

Findings

Smarr formula holds regardless of conical singularities.

First law of thermodynamics applies only without conical singularities.

Solutions with background magnetic fields are also presented.

Abstract

We construct black ring solutions in five-dimensional $U(1)^3$ supergravity which carry three dipole charges, three electric charges and one angular momentum parameter. These solutions are written in a form that is sufficiently compact that their global and thermodynamic properties can be studied explicitly. In particular, we find that the Smarr formula is obeyed regardless of whether or not conical singularities are present, whereas the first law of thermodynamics holds only in the absence of conical singularities. We also present black ring solutions with three background magnetic fields.