AdS and Lifshitz scalar hairy black holes in Gauss-Bonnet gravity

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 (φ) = 2Λ 0 + 1 2 m 2 φ 2 + γ 4 φ 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.

On the Noether charge and the gravity duals of quantum complexity

“…We conclude in section 5. [24,25,26,27,28,29,30,31,32,33,34,35,36,37]). To begin our story, let us first review how the Noether charge is introduced in the Wald-Iyer formalism.…”

Note on the Noether charge and holographic transports

“…The method is known as Wald formalism in literature. Recently, it has been applied to study the first laws of a variety of hairy black holes [32,33,34,35,36,37,38,39,40,41,42,43,44,45]. In particular, it was established in [29] that the holographic heat current excited by transverse perturbations δg tx i , δA x i with a linear time dependence was simply given by the Noether charge at asymptotic infinity (see Eq.(9)).…”

“…It should be emphasized that the above result is valid as well when there are non-minimal couplings between the metric and the matter fields, with the Noether charge and the equations of motions including extra terms associated to the non-minimal couplings. We refer the readers to literatures [41,42,43,44,45] for more details on this point. It becomes clear that the Noether charge Q rx i is closely related to the dynamical equations of the transverse perturbations (δg tx i , δA x i ).…”

Static and dynamic charged black holes

“…The construction of analytic dynamical solutions is propelled by the recent constructions of static black holes in a variety theories [13][14][15][16][17][18][19][20][21]. Some of these solutions can be promoted to become dynamical ones where the static black holes are the end points of the time evolution [19,20].…”