Solution Generation of a Capped Black Hole

Abstract

Utilizing the electric Harrison transformation developed in five-dimensional minimal supergravity, we construct an exact solution characterizing non-BPS charged rotating black holes with a horizon cross-section of a lens space L(n;1). Among these solutions, only the ones corresponding to n=0 and n=1 do not have any curvature singularities, conical singularities, Dirac-Misner string singularities, and orbifold singularities both on and outside the horizon; additionally, it is free from closed timelike curves. The solution for n=0 corresponds to the charged dipole black ring that we constructed in the previous paper. The specific solution for n=1, referred to as the ``capped black hole," was introduced in our previous letter. This provides the first example of a non-BPS exact solution, representing an asymptotically flat, stationary spherical black hole with a domain of outer communication (DOC) having a nontrivial topology in five-dimensional minimal supergravity. We demonstrate that the DOC on a timeslice has the topology of $[R^4\# CP^2 ]\setminus B^4$. Differing from the well-known Myers-Perry and Cveti\v{c}-Youm black holes describing a spherical horizon topology and a DOC with a trivial topology of $R^4 \setminus B^4$ on a timeslice, the capped black hole's horizon is capped by a disc-shaped bubble. We explicitly demonstrate that the capped black hole carries mass, two angular momenta, an electric charge, and a magnetic flux, with only three of these quantities being independent. Furthermore, we reveal that this black hole can possess identical conserved charges as the Cveti\v{c}-Youm black hole. The existence of this solution challenges black hole uniqueness beyond both the black ring and the BPS spherical black hole. Moreover, within specific parameter regions, the capped black hole can exhibit a larger entropy than the Cveti\v{c}-Youm black hole.