Black hole chemistry, the cosmological constant and the embedding tensor

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.

References added, 43 pages, no figures

References in corpus (13)

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• Gauge Theories, Duality Relations and the Tensor Hierarchy
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• The first law and Wald entropy formula of heterotic stringy black holes at first order in alpha prime
• Komar integrals for theories of higher order in the curvature and black-hole chemistry
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• The end of the p-form hierarchy
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Cited by in corpus (8)

• Higher-dimensional origin of extended black hole thermodynamics
• Extended black hole thermodynamics from extended Iyer-Wald formalism
• Coupling Constants as Conserved Charges in Black Hole Thermodynamics
• On scalar charges and black-hole thermodynamics
• Non-closed scalar charge in four-dimensional Einstein-scalar-Gauss-Bonnet black hole thermodynamics
• A note on the Noether-Wald and generalized Komar charges
• Extended symmetry of the Maxwell theory with a gauge coupling constant as a conserved charge
• Modified first law of charged dilaton black hole