Exact black hole solutions in higher-order scalar-tensor theories

TL;DR

This paper explores explicit black hole solutions in higher-order scalar-tensor theories, including stealth and non-stealth solutions, and introduces a disformed Kerr metric that departs from standard GR predictions.

Contribution

It provides new analytic black hole solutions in scalar-tensor theories, including the disformed Kerr metric, and classifies solutions derived from higher-dimensional Lovelock theories.

Findings

Stealth solutions with Ricci-flat metrics and non-trivial scalar fields.

Disformed Kerr metric as a measurable departure from Kerr geometry.

Classification of solutions based on Kaluza-Klein reduction properties.

Abstract

In this chapter, we discuss explicit black hole solutions in higher-order scalar-tensor theories. After a brief recap of no-hair theorems, we start our discussion by so-called stealth solutions present in theories with parity and shift symmetry. Stealth solutions are such that their metric are Ricci flat General Relativity solutions, but they are accompanied by a non-trivial scalar field, in both spherically-symmetric and rotating cases. The stealth metrics then enable to construct an analytic stationary solution of scalar-tensor theory which is called disformed Kerr metric. This solution constitutes a measurable departure from the usual Kerr geometry of GR. We discuss within parity and shift symmetric theories several non-stealth solutions. We then consider scalar-tensor theories stemming from a Kaluza-Klein reduction of a higher-dimensional Lovelock theory. These theories encompass all Horndeski functionals and hence go beyond parity and shift symmetry. Reduction and singular limits allow one to obtain non-stealth black holes with differing interesting properties which are not Ricci flat metrics. We analyse the solutions obtained and classify them with respect to the geometry of the internal space according to their Kaluza-Klein origin.