Planar AdS black holes in Lovelock gravity with a nonminimal scalar field

TL;DR

This paper constructs planar AdS black hole solutions in Lovelock gravity with a nonminimal scalar field, revealing new classes of solutions that depend on higher-order curvature terms and include stealth configurations and matter couplings.

Contribution

It introduces novel AdS black hole solutions in Lovelock gravity with nonminimal scalar fields, including stealth configurations and solutions with multiple (D-1)-forms, extending previous models.

Findings

Two classes of AdS black hole solutions with planar horizons are derived.

Stealth black hole configurations are identified and related to Kerr-Schild transformations.

Solutions with multiple (D-1)-forms are obtained for arbitrary nonminimal coupling.

Abstract

In arbitrary dimension D, we consider a self-interacting scalar field nonminimally coupled with a gravity theory given by a particular Lovelock action indexed by an integer k. To be more precise, the coefficients appearing in the Lovelock expansion are fixed by requiring the theory to have a unique AdS vacuum with a fixed value of the cosmological constant. This yields to k=1,2,...,[(D-1)/2] inequivalent possible gravity theories; here the case k=1 corresponds to the standard Einstein-Hilbert Lagrangian. For each par (D,k), we derive two classes of AdS black hole solutions with planar event horizon topology for particular values of the nonminimal coupling parameter. The first family of solutions depends on a unique constant and is valid only for k>1. In fact, its GR counterpart k=1 reduces to the pure AdS metric with a vanishing scalar field. The second family of solutions involves two independent constants and corresponds to a stealth black hole configuration; that is a nontrivial scalar field together with a black hole metric such that both side of the Einstein equations (gravity and matter parts) vanishes identically. In this case, the standard GR case k=1 reduces to the Schwarzschild-AdS-Tangherlini black hole metric with a trivial scalar field. In both cases, the existence of these solutions is strongly inherent of the presence of the higher order curvature terms k>1 of the Lovelock gravity. We also establish that these solutions emerge from a stealth configuration defined on the pure AdS metric through a Kerr-Schild transformation. Finally, in the last part, we include multiple exact (D-1)-forms homogenously distributed and coupled to the scalar field. For a specific coupling, we obtain black hole solutions for arbitrary value of the nonminimal coupling parameter generalizing those obtained in the pure scalar field case.