AdS and Lifshitz Scalar Hairy Black Holes in Gauss-Bonnet Gravity

TL;DR

This paper constructs and analyzes various scalar hairy black hole solutions in Gauss-Bonnet gravity, including AdS and Lifshitz types, exploring their thermodynamics, stability, and dynamical evolution.

Contribution

It introduces new classes of AdS and Lifshitz black holes with scalar hair in Gauss-Bonnet gravity, including thermodynamic and dynamical properties, at the critical point of the theory.

Findings

Scalar hair contributes to black hole thermodynamics.

Existence of Lifshitz vacua at the critical point.

Construction of dynamical solutions describing radiating black holes.

Abstract

We consider Gauss-Bonnet (GB) gravity in general dimensions, which is non-minimally coupled to a scalar field. By choosing the scalar potential of the type $V(\phi)=2\Lambda_0+\fft 12m^2\phi^2+\gamma_4\phi^4$, we first obtain large classes of scalar hairy black holes with spherical/hyperbolic/planar topologies that are asymptotic to locally anti-de Sitter (AdS) space-times. We derive the first law of black hole thermodynamics using Wald formalism. In particular, for one class of the solutions, the scalar hair forms a thermodynamic conjugate with the graviton and nontrivially contributes to the thermodynamical first law. We observe that except for one class of the planar black holes, all these solutions are constructed at the critical point of GB gravity where there exists an unique AdS vacua. In fact, Lifshitz vacuum is also allowed at the critical point. We then construct many new classes of neutral and charged Lifshitz black hole solutions for a either minimally or non-minimally coupled scalar and derive the thermodynamical first laws. We also obtain new classes of exact dynamical AdS and Lifshitz solutions which describe radiating white holes. The solutions eventually become an AdS or Lifshitz vacua at late retarded times. However, for one class of the solutions the final state is an AdS space-time with a globally naked singularity.