On scalar charges and black-hole thermodynamics

Abstract

We revisit the first law of black hole thermodynamics in 4-dimensional theories containing scalar and Abelian vector fields coupled to gravity using Wald's formalism and a new definition of scalar charge as an integral over a 2-surface which satisfies a Gauss law in stationary black-hole spacetimes. We focus on ungauged supergravity-inspired theories with symmetric sigma models whose symmetries generate electric-magnetic dualities leaving invariant their equations of motion. Our manifestly duality-invariant form of the first law is compatible with the one obtained by of Gibbons, Kallosh and Kol. We also obtain the general expression for the scalar charges of a stationary black hole in terms of the other physical parameters of the solution and the position of the horizon, generalizing the expression obtained by Pacilio for dilaton black oles.

Misprints corrected and a few comments and references added. Version to be published in JHEP

References in corpus (9)

• Surface charge algebra in gauge theories and thermodynamic integrability
• The supersymmetric configurations of N=2, d=4 supergravity coupled to vector supermultiplets
• Note on the First Law with p-form potentials
• Redundant and Physical Black Hole Parameters: Is there an independent physical dilaton charge?
• Magnetic charges and Wald entropy
• Black hole chemistry, the cosmological constant and the embedding tensor
• Komar integral and Smarr formula for axion-dilaton black holes versus S duality
• Non-extremal, ${\alpha }^{\prime }$-corrected black holes in 5-dimensional Heterotic Superstring Theory
• Gauge Invariant Derivation of Zeroth and First Laws of Black Hole Thermodynamics

Cited by in corpus (8)

• Boundary terms and conserved charges in higher-derivative gauged supergravity
• Non-closed scalar charge in four-dimensional Einstein-scalar-Gauss-Bonnet black hole thermodynamics
• Gravitational Atoms from Topological Stars
• On the interactions and equilibrium between Einstein-Maxwell-Dilaton black holes
• A note on the Noether-Wald and generalized Komar charges
• On the generalized Komar charge of Kaluza-Klein theories and higher-form symmetries
• Electric and dilatonic fields of a charged massive particle at rest in the field of a charged dilaton black hole
• From rotating attractors to extremal black holes with axionic hair