Exact black holes and black branes with bumpy horizons supported by superfluid pions

Abstract

We present exact solutions of the Einstein-$SU(2)$ non-linear sigma model in $3+1$ spacetime dimensions, describing bumpy black holes and black branes. Using an Ansatz for superfluid pion multi-vortices, the matter sector reduces to a first-order BPS system, while the Einstein equations reduce to a Liouville equation with a smooth source governing the horizon deformation. These solutions describe horizons of different constant curvatures, with nontrivial bumpy geometries protected by an integer topological invariant, namely the vorticity, which also controls the number of bumps and the black hole thermodynamics. Remarkably, such horizons arise in a minimal and physically motivated matter model, without invoking exotic fields or modified gravity. The physical implications of these results in holography and astrophysics are briefly described.