Theory HEP Seminar

Enthalpy and Thermodynamics of Lovelock Black Holes:
extended First Law and Smarr Mass Formula

Jennie Traschen

University of Massachusetts

The Smarr formulae are exact relations between the mass, area, and other geometrical properties of static (or stationary) black holes. The method of derivation for an asymptotically flat black hole runs into problems with infinities if the spacetime is asymptotically anti-deSitter. In this talk, we will show how the constraint equations “tame the infinities” in a natural way, and derive the mass formula for static AdS black holes in Lovelock (higher curvature) gravity. An intermediate step is to first prove an extended version of the first law that includes the variation in all dimensionful parameters of the theory. The good news is that in the special case of Einstein gravity with cosmological constant one finds a ?pressure-volume? work term, where the volume is an effective volume of the black hole, and the pressure comes from the cosmological constant. This of course meshes nicely with classical thermodynamics. The bad news is that we study this for a general Lovelock theory &emdash; but happily, long tedious equations will not be allowed. The mass formula is used to derive an expression for the free energy a spherically symmetric Lovelock black hole in terms of the horizon radius and the Lagrangian parameters, without knowing the solutions to the field equations. We will discuss applications to studying phase transitions.