Non-extremal black holes of N=2, d=5 supergravity

We study the generalization of the Ansatz of Galli et al. (2011) [1] for non-extremal black holes of N=2, d=4 supergravities for a simple model of N=2, d=5 supergravity with a vector multiplet whose moduli space has two branches. We use the formalism of Ferrara, Gibbons and Kallosh (1997) [2], which we generalize to any dimension d. We find that the equations of motion of the model studied can be completely integrated without the use of our Anstaz (which is, nevertheless, recovered in the integration). The family of solutions found (common to both branches) is characterized by five independent parameters: the mass M, the electric charges q0, q1, the asymptotic value of the scalar at infinity ϕ∞ and the scalar charge Σ. The solutions have a singular horizon whenever Σ differs from a specific expression Σ0(M,q0,q1,ϕ∞) (i.e. when there is primary scalar hair Σ−Σ0≠0). The family of regular black holes interpolates between its two extremal limits. The supersymmetry properties of the extremal solutions depend on the choice of branch: one is always supersymmetric and the other non-supersymmetric in one branch and the reverse in the other one.