Plebański-Demiański solutions in quadratic gravity with conformally coupled scalar fields
Adolfo Cisterna, Aníbal Neira-Gallegos, Julio Oliva, Scarlett C. Rebolledo-Caceres
Abstract
We show that the Pleba\ifmmode \acute{n}\else \'{n}\fi{}ski-Demia\ifmmode \acute{n}\else \'{n}\fi{}ski spacetime persists as a solution of general relativity when the theory is supplemented with both, a conformally coupled scalar theory and with quadratic curvature corrections. The quadratic terms are of two types and are given by quadratic combinations of the Riemann tensor as well as a higher curvature interaction constructed with a scalar field which is conformally coupled to quadratic terms in the curvature. The later is built in terms of a four-rank tensor ${{S}_{\ensuremath{\mu}\ensuremath{\nu}}}^{\ensuremath{\lambda}\ensuremath{\rho}}$ that depends on the Riemann tensor and the scalar field, and that transforms covariantly under local Weyl rescalings. Due to the generality of the Pleba\ifmmode \acute{n}\else \'{n}\fi{}ski-Demia\ifmmode \acute{n}\else \'{n}\fi{}ski family, several new hairy black hole solutions are obtained in this higher curvature model. We pay particular attention to the C-metric spacetime and the stationary Taub-NUT metric, which in the hyperbolic case can be analytically extended leading to healthy, asymptotically AdS, wormhole configurations. Finally, we present a new general model for higher derivative, conformally coupled scalars, depending on an arbitrary function and that we have dubbed conformal $K$ essence. We also construct spherically symmetric hairy black holes for these general models.