Smarr formula for black holes endowed with both electric and magnetic charges

Abstract: The present paper clarifies how to consistently take into account the contribution of magnetic charges in the generalized Smarr mass formula by using properly the Tomimatsu's representation of Komar integrals. It is shown in particular that in all three examples of the dyonic solutions considered by us, the sum of the two electromagnetic terms in Smarr's formula can be cast into the form $\bar{\cal Q}\Phi^H_{ext}$, where ${\cal Q}$ is the complex charge and $\Phi^H_{ext}$ the complex extension of the electric potential.