New black holes in $D=5$ minimal gauged supergravity: Deformed boundaries and frozen horizons

A new class of black hole solutions of the five-dimensional minimal gauged supergravity is presented. They are characterized by the mass, the electric charge, two equal magnitude angular momenta and the magnitude of the magnetic potential at infinity. These black holes possess a horizon of spherical topology; however, both the horizon and the sphere at infinity can be arbitrarily squashed, with nonextremal solutions interpolating between black strings and black branes. A particular set of extremal configurations corresponds to a new one-parameter family of supersymmetric black holes. While their conserved charges are determined by the squashing of the sphere at infinity, these supersymmetric solutions possess the same horizon geometry.

Figure 1

The $(T_H,A_H)$-domain of existence of static vacuum black holes with a deformed sphere at infinity. The inset shows the horizon deformation ${\epsilon }_H$ for several values of the boundary squashing ${\epsilon }_B$.

Figure 2

The $(T_H,{\epsilon }_B,{\epsilon }_H)$-domain of existence is shown for a particular set of black holes. The $(Q,J,{\mathrm{\Phi }}_m)$-dependence of the boundary squashing parameter ${\epsilon }_B$ is imposed such that the extremal limit corresponds to supersymmetric solutions [e.g. ${\mathrm{\Phi }}_m=L({\epsilon }_B^2-1)/2\sqrt{3}$]. Color curves are isolines of constant ${\epsilon }_B$, and grey curves are isolines of constant ${\epsilon }_H$.

Figure 3

The $(T_H,{\epsilon }_H,A_H)$-diagram for the same solutions as in Fig. 2. The full set of SUSY solutions is mapped here to a single point, possessing the same horizon area and deformation. Isolines of constant ${\epsilon }_B$ and $A_H$ are marked with color and grey lines, respectively.

Figure 4

The $(Q,J,M)$-diagram is shown for three families of supersymmetric AdS solutions.