Charging a double Kerr solution in five-dimensional Einstein–Maxwell–Kalb–Ramond theory

Abstract

We consider the low-energy effective action of the five-dimensional (5D) Einstein–Maxwell–Kalb–Ramond theory. After compactifying this truncated model on a two-torus and switching off the U(1) vector fields of this theory, we recall a formulation of the resulting three-dimensional action as a double Ernst system coupled to gravity. Further, by applying the so-called normalized Harrison transformation on a generic solution of this double Ernst system we recover the U(1) vector field sector of the theory. Afterward, we compute the field content of the generated charged configuration for the special case when the starting Ernst potentials correspond to a pair of interacting Kerr black holes, obtaining in this way an exact field configuration of the 5D Einstein–Maxwell–Kalb–Ramond theory endowed with effective Coulomb and dipole terms with momenta. Some physical properties of this object are analyzed as well as the effect of the normalized Harrison transformation on the double Kerr seed solution.