Conformally coupled scalar in Lovelock theory

TL;DR

This paper explores black hole solutions with conformally coupled scalar fields in higher-dimensional Lovelock gravity, revealing stealth configurations and methods to generate non-conformal models with new black hole solutions.

Contribution

It demonstrates the existence of stealth black hole solutions with conformally coupled scalars in higher-dimensional Lovelock gravity and introduces a procedure to derive non-conformal models with new solutions.

Findings

Existence of stealth black hole solutions with scalar charge.

Extension to time-dependent scalar fields in non shift-symmetric theories.

Method to obtain non-conformal actions and solutions from conformal models.

Abstract

In arbitrary higher dimension, we consider the combination of Lovelock gravity alongside a scalar-tensor action built out of higher order operators and Euler densities. The latter action is constructed in such a way as to ensure conformal invariance for the scalar field. For the combined version of these theories, we show the existence of black hole solutions interpreted as stealth configurations within Lovelock gravity theory. The scalar field solutions are endowed with an integration constant that may be identified as a scalar charge. In particular, we show that these stealth solutions can be extended to include a time-dependent scalar field despite the underlying theory being non shift-symmetric. Finally, we present a procedure to obtain a non-conformally invariant action in even dimensions from the considered theory. For the target theory, the scalar field is not conformally coupled to gravity although the scalar field equation itself is conformally invariant. By means of this procedure, the black hole stealth configurations are converted into non-stealth black hole solutions, as discovered recently in four dimensions.