Black holes, parallelizable horizons and half-BPS states for the Einstein-Gauss-Bonnet theory in five dimensions

TL;DR

This paper constructs exact vacuum solutions with torsion in five-dimensional Einstein-Gauss-Bonnet theory, revealing supersymmetric black hole ground states with a parallelized three-sphere base manifold, highlighting torsion's role in supersymmetry.

Contribution

It introduces a class of static black hole solutions with torsion in five-dimensional Einstein-Gauss-Bonnet gravity, linking the Gauss-Bonnet coupling to a Chern-Simons form and identifying half-BPS states.

Findings

Solutions fix the Gauss-Bonnet coupling to a Chern-Simons form.

Ground state is a half-BPS black hole with a parallelized three-sphere.

Explicit Killing spinors demonstrate supersymmetry in the solutions.

Abstract

Exact vacuum solutions with a nontrivial torsion for the Einstein-Gauss-Bonnet theory in five dimensions are constructed. We consider a class of static metrics whose spacelike section is a warped product of the real line with a nontrivial base manifold endowed with a fully antisymmetric torsion. It is shown requiring solutions of this sort to exist, fixes the Gauss-Bonnet coupling such that the Lagrangian can be written as a Chern-Simons form. The metric describes black holes with an arbitrary, but fixed, base manifold. It is shown that requiring its ground state to possess unbroken supersymmetries, fixes the base manifold to be locally a parallelized three-sphere. The ground state turns out to be half-BPS, which could not be achieved in the absence of torsion in vacuum. The Killing spinors are explicitly found.