Plebanski-Demianski solutions in quadratic gravity with conformally coupled scalar fields

We show that the Plebanski-Demianski 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-mu nu(lambda 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 Plebanski-Demianski 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.

Automated summary

The study demonstrates that the Plebanski-Demianski spacetime remains a solution of general relativity when supplemented with both a conformally coupled scalar theory and quadratic curvature corrections. The research also involves obtaining new hairy black hole solutions and analytically extending specific metric spacetimes to produce healthy asymptotically AdS wormhole configurations.