Black hole chemistry, the cosmological constant and the embedding tensor

TL;DR

This paper explores the thermodynamics of black holes in theories with dimensionful constants, promoting these constants to scalar fields and linking them to the embedding tensor, revealing new dualities and thermodynamic variables.

Contribution

It introduces a method to treat constants like the cosmological constant as scalar fields and connects the embedding tensor to black-hole thermodynamics in supergravity theories.

Findings

Embedding tensor acts as a thermodynamic variable in the Smarr formula.

Scalar fields can replace constants, providing a dual description.

Link established between black-hole thermodynamics and supergravity gaugings.

Abstract

We study black-hole thermodynamics in theories that contain dimensionful constants such as the cosmological constant or coupling constants in Wald's formalism. The most natural way to deal with these constants is to promote them to scalar fields introducing a (d-1)-form Lagrange multiplier that forces them to be constant on-shell. These (d-1)-form potentials provide a dual description of them and, in the context of superstring/supergravity theories, a higher-dimensional origin/explanation. In the context of gauged supergravity theories, all these constants can be collected in the embedding tensor. We show in an explicit 4-dimensional example that the embedding tensor can also be understood as a thermodynamical variable that occurs in the Smarr formula in a duality-invariant fashion. This establishes an interesting link between black-hole thermodynamics, gaugings and compactifications in the context of superstring/supergravity theories.