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  • Open Access

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

Fabrizio Canfora*

Andrés Gomberoff†

Carla Henríquez-Baez‡

Aldo Vera§

  • Facultad de Ciencias, Ingeniería y Tecnología, Universidad Mayor, Avenida Manuel Montt 367, Santiago, Chile and Centro Multidisciplinario de Física, Vicerrectoría de Investigación, Universidad Mayor, Camino La Pirámide 5750, Santiago, Chile

  • Centro Multidisciplinario de Física, Vicerrectoría de Investigación, Universidad Mayor, Camino La Pirámide 5750, Santiago, Chile

  • Núcleo de Matemática, Física y Estadística, Universidad Mayor, Avenida Manuel Montt 367, Santiago, Chile and Centro Multidisciplinario de Física, Vicerrectoría de Investigación, Universidad Mayor, Camino La Pirámide 5750, Santiago, Chile

  • *Contact author: fabrizio.canfora@uss.cl
  • †Contact author: andres.gomberoff@umayor.cl
  • ‡Contact author: carla.henriquez@umayor.cl
  • §Contact author: aldo.vera@umayor.cl
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Phys. Rev. D 113, 084068 – Published 30 April, 2026

DOI: https://doi.org/10.1103/9shw-n7rs

Abstract

We present exact solutions of the Einstein–SU(2) nonlinear sigma model in 3+1 spacetime dimensions, describing bumpy black holes and black branes. Using an Ansatz for superfluid pion multivortices, the matter sector reduces to a first-order Bogomol’nyi–Prasad–Sommerfield 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.

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Phys. Rev. D 113, 084068– Published 30 April, 2026
  • Received 5 February 2026
  • Accepted 13 April 2026
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