Komar integral and Smarr formula for axion-dilaton black holes versus S duality

Abstract

We construct the Komar integral for axion-dilaton gravity using Wald's formalism and momentum maps and we use it to derive a Smarr relation for stationary axion-dilaton black holes. While the Wald-Noether 2-form charge is not invariant under SL(2,R) electric-magnetic duality transformations because Wald's formalism does not account for magnetic charges and potentials, the Komar integral constructed with it turns out to be invariant and, in more general theories, it will be fully symplectic invariant. We check the Smarr formula obtained with the most general family of static axion-dilaton black holes.

LaTeX file, 19 pages, no figures

References in corpus (6)

• Smarr Formula and an Extended First Law for Lovelock Gravity
• The supersymmetric configurations of N=2, d=4 supergravity coupled to vector supermultiplets
• Komar Integrals in Higher (and Lower) Derivative Gravity
• The first law and Wald entropy formula of heterotic stringy black holes at first order in alpha prime
• The first law of heterotic stringy black hole mechanics at zeroth order in alpha prime
• General theory of Lie derivatives for Lorentz tensors

Cited by in corpus (7)

• On scalar charges and black-hole thermodynamics
• Magnetic charges and Wald entropy
• Black hole chemistry, the cosmological constant and the embedding tensor
• Corrections to Extremal Black Holes from Iyer-Wald Formalism
• Non-closed scalar charge in four-dimensional Einstein-scalar-Gauss-Bonnet black hole thermodynamics
• On the interactions and equilibrium between Einstein-Maxwell-Dilaton black holes
• A note on the Noether-Wald and generalized Komar charges