AdS and Lifshitz black holes in conformal and Einstein-Weyl gravities

Abstract

We study black hole solutions in extended gravities with higher-order curvature terms, including conformal and Einstein-Weyl gravities. In addition to the usual AdS vacuum, the theories admit Lifshitz and Schrödinger vacua. The AdS black hole in conformal gravity contains an additional parameter over and above the mass, which may be interpreted as a massive spin-2 hair. By considering the first law of thermodynamics, we find that it is necessary to introduce an associated additional intensive/extensive pair of thermodynamic quantities. We also obtain new Liftshitz black holes in conformal gravity and study their thermodynamics. We use a numerical approach to demonstrate that AdS black holes beyond the Schwarzschild-AdS solution exist in Einstein-Weyl gravity. We also demonstrate the existence of asymptotically Lifshitz black holes in Einstein-Weyl gravity. The Lifshitz black holes arise at the boundary of the parameter ranges for the AdS black holes. Outside the range, the solutions develop naked singularities. The asymptotically AdS and Lifshitz black holes provide an interesting phase transition, in the corresponding boundary field theory, from a relativistic Lorentzian system to a non-relativistic Lifshitz system.

Thermodynamic and classical instability of AdS black holes in fourth-order gravity

“…On the other hand, for M 2 d = −0.013 < 0(m 2 d = 0.02 < 6/ 2 ) which is dominantly described by conformal gravity [41], the small black hole (r + < r * ) is thermodynamically stable because C dADT > 0, while the large black hole (r + > r * ) is thermodynamically unstable because C dADT < 0. See the dotted (unfamiliar) curves in figure 3 for observation.…”

Spectroscopy of z=0 Lifshitz Black Hole

“…The Lifshitz BH solutions exist in the CG theory for both = 4 and = 0 [26,43]; however, when = 3 and = 4, Lifshitz BHs appear in the Horava-Lifshitz gravity [26,44,45]. Now, we focus on the 0LBH of the CG theory whose metric is given by [26]:…”

“…In this section, we introduce the four-dimensional Lifshitz spacetime and its special case, that is, 0LBH [26]. Conformal gravity (CG) covers gravity theories that are invariant under Weyl transformations.…”

“…The Lifshitz BHs are invariant under anisotropic scale and characterize the gravitational dual of strange metals [42]. The action of the Einstein-Weyl gravity [26] is given by…”

“…This study mainly explores the entropy/area spectra of a four-dimensional Lifshitz BH [26] possessing a particular dynamical exponent = 0. To analyze the physical features of the = 0 Lifshitz BH ( 0LBH) geometry, we first calculate its quasi-local mass [27] and temperature via Wald's entropy [28] and statistical Hawking temperature formula 2 Advances in High Energy Physics [29,30], respectively.…”