Three-dimensional charged Einstein-aether black holes and Smarr formula

TL;DR

This paper introduces new exact charged black hole solutions in three-dimensional Einstein-aether gravity, explores their thermodynamics including Smarr formulas, and discusses implications for holography under Lorentz violation.

Contribution

The paper presents two new classes of exact charged solutions in 3D Einstein-aether gravity and derives their thermodynamic properties, extending black hole thermodynamics to universal horizons.

Findings

Universal horizons obey a form of the first law of black hole mechanics.

Black hole mass can be interpreted as spacetime enthalpy.

Solutions include BTZ black holes with universal horizons.

Abstract

We investigate the three-dimensional behavior of gravity coupled to a dynamical unit timelike vector: the aether, and present two new classes of exact charged solutions. When c_{13}=0,\Lambda'=0$, we find the solutions is the usual BTZ black hole but now with an universal horizon. In the frame of black hole chemistry, we then calculate the temperature of the universal horizons and, construct the Smarr formulas and first law in the three cases: quasi-asymptotically flat, aether asymptotically flat and quasi-BTZ black hole spacetime. We found these universal horizons obey an exact (or slightly modified) first law of black hole mechanics and may have an entropy and, black hole mass can be interpreted as enthalpy of spacetime. Then the holography may be extended to these horizons under violating Lorentz symmetry.