Gravitational Tension and Thermodynamics of Planar AdS Spacetimes

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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.