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We revisit the derivation by Tomimatsu of the generalized Komar integralsgiving the mass and angular momentum of rotating Einstein-Maxwell black holes.We show that, contrary to Tomimatsu's claim, the usual Smarr formula relatingthe horizon mass and angular momentum still holds in the presence of bothelectric and magnetic charges. The simplest case is that of dyonic Kerr-Newmanblack holes, for which we recover the modified Smarr formula relating theasymptotic mass and angular momentum, the difference between asymptotic andhorizon masses being equal to the sum of the two Dirac string masses. Ourresults apply in particular to the case of dyonic dihole solutions which havebeen investigated recently.

On the Smarr formula for rotating dyonic black holes