AdS and Lifshitz Black Holes in Conformal and Einstein-Weyl Gravities

TL;DR

This paper explores black hole solutions in extended gravity theories with higher-order curvature terms, revealing new AdS and Lifshitz black holes, their thermodynamics, and phase transitions in the boundary field theories.

Contribution

It introduces new AdS and Lifshitz black hole solutions in conformal and Einstein-Weyl gravities, analyzing their thermodynamics and phase transitions.

Findings

Existence of AdS black holes with additional parameters in conformal gravity.

Discovery of Lifshitz black holes in conformal and Einstein-Weyl gravities.

Phase transition from relativistic to non-relativistic systems in boundary theories.

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 Schr\"odinger 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.