Black holes with topological charges in Chern-Simons AdS$_5$ supergravity

TL;DR

This paper investigates static black hole solutions with topological charges in five-dimensional Chern-Simons supergravity, revealing novel soliton structures, topological features, and supersymmetry properties.

Contribution

It introduces new topologically charged black hole solutions in 5D Chern-Simons supergravity with detailed analysis of their properties and supersymmetry.

Findings

Solutions include black holes, naked singularities, and AdS spaces.

Presence of nontrivial $SU(2)$ solitons with Pontryagin index.

Extremal limit features soliton-antisoliton unwinding and BPS states.

Abstract

We study static black hole solutions with locally spherical horizons coupled to non-Abelian field in $\mathcal{N}=4$ Chern-Simons AdS$_5$ supergravity. They are governed by three parameters associated to the mass, axial torsion and amplitude of the internal soliton, and two ones to the gravitational hair. They describe geometries that can be a global AdS space, naked singularity or a (non-)extremal black hole. We analyze physical properties of two inequivalent asymptotically AdS solutions when the spatial section at radial infinity is either a 3-sphere or a projective 3-space. An important feature of these 3-parametric solutions is that they possess a topological structure including two $SU(2)$ solitons that wind nontrivially around the black hole horizon, as characterized by the Pontryagin index. In the extremal black hole limit, the solitons' strengths match and a soliton-antisoliton system unwinds. That limit admits both non-BPS and BPS configurations. For the latter, the pure gauge and non-pure gauge solutions preserve $1/2$ and $1/16$ of the original supersymmetries, respectively. In a general case, we compute conserved charges in Hamiltonian formalism, finding many similarities with standard supergravity black holes.