Black Rings in Supergravity

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.