Gravitational Tension and Thermodynamics of Planar AdS Spacetimes

TL;DR

This paper derives new thermodynamic relations for planar AdS black holes and solitons, revealing a symmetry between black holes and bubbles and implications for dual gauge theories.

Contribution

It introduces novel Smarr formulas incorporating tensions and thermodynamic volumes for planar AdS spacetimes, highlighting a symmetry between phases.

Findings

Sum of ADM mass and tensions vanishes for planar AdS spacetimes.

Smarr formulas relate mass, tensions, horizon and bubble areas, and thermodynamic volumes.

Symmetry between black holes and bubbles suggests a dual gauge theory phase symmetry.

Abstract

We derive new thermodynamic relations for asymptotically planar AdS black hole and soliton solutions. In addition to the ADM mass, these spacetimes are characterized by gravitational tensions in each of the planar spatial directions. We show that with planar AdS asymptotics, the sum of the ADM mass and tensions necessarily vanishes, as one would expect from the AdS /CFT correspondence. Each Killing vector of such a spacetime leads to a Smarr formula relating the ADM mass and tensions, the black hole horizon and soliton bubble areas, and a set of thermodynamic volumes that arise due to the non-vanishing cosmological constant. These Smarr relations display an interesting symmetry between black holes and bubbles, being invariant under the simultaneous interchange of the mass and black hole horizon area with the tension and soliton bubble area. This property may indicate a symmetry between the confining and deconfined phases of the dual gauge theory.