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

TL;DR

This paper demonstrates that Plebanski-Demianski solutions remain valid in quadratic gravity with conformally coupled scalar fields, leading to new hairy black hole solutions and wormhole configurations in higher curvature models.

Contribution

It introduces a generalized higher curvature model with conformally coupled scalars, extending known solutions and constructing new hairy black holes and wormholes.

Findings

Plebanski-Demianski solutions persist in quadratic gravity with scalar fields.

New hairy black hole solutions are obtained in the extended model.

Asymptotically AdS wormhole configurations are constructed.

Abstract

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 rescallings. 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.