Mass formulas for supergravity black holes with string singularities

We extend the derivation of mass formulas for stationary axisymmetric asymptotically locally flat solutions with string singularities on the polar axis to general supergravity actions containing vector and scalar fields. It is based on the rod structure of the solutions in Weyl coordinates and is applicable to black holes with Dirac and Misner strings. The obtained formulas differ from the corresponding ones in Einstein–Maxwell theory only by summation over all independent electric charges.