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

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 threesphere. 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.

Black hole solutions in Chern-Simons AdS supergravity

“…Defining the new function η(r) as 19) eq. (3.14) reads 20) where 21) and, by the same token, L 0i = 0 and L 1i = 0 are automatically satisfied as well.…”

“…and the solution (3.23)-(3.31) reduces to ψ r = 0, φ(r) = 2Cr 2 , with f 2 (r) = r 2 /ℓ 2 − C 2 , which turns out to be a special case of the solution found in ref. [20]. In the next section we discuss the relation with that solution in more detail.…”

“…For example, in ref. [20], a solution with a metric of the form (3.1) and axial torsion (φ(r) = 0) was considered. That solution, however, is uncharged and so it does not require (and does not include) other components of the torsion (ψ p or χ q ).…”

“…[20] that possesses only the axial component of torsion. As mentioned before, the axial-torsion solution and the one presented in section 3 coincide at a particular point of the space of solutions.…”

“…More precisely, a special case of our solution (3.23)-(3.31) coincides with the axial-torsion one (see eqs. (19)- (20) in [20] and/or eqs. (4.1)-(4.1) below).…”