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

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