Komar integrals for theories of higher order in the curvature and black-hole chemistry

Abstract

We construct Komar-type integrals for theories of gravity of higher order in the Riemann curvature coupled to simple kinds of matter (scalar and vector fields) and we use them to compute Smarr formulae for black-hole solutions in those theories. The equivalence between f(R) and Brans-Dicke theories is used to argue that the dimensionful parameters that appear in scalar potentials must be interpreted as thermodynamical variables ("pressures") and we give a general expression for their conjugate potentials ("volumes"}.