String theory extensions of Einstein–Maxwell fields: The stationary case

We present a new approach for generating solutions in heterotic string theory compactified down to three dimensions on a torus with $d+n>2,$ where $d$ and $n$ stand for the number of compactified space–time dimensions and Abelian gauge fields, respectively. It is shown that in the case when $d=2k+1,$ and $n$ is arbitrary, one can apply a solution-generating procedure which consists of mapping seed solutions of the stationary Einstein theory with $k$ Maxwell fields to the heterotic string realm by using pure field redefinitions. A novel feature of this method is that it is precisely the electromagnetic sector of the stationary electrovacuum that mainly gives rise to a nontrivial multidimensional metric. This approach leads to classes of solutions which are invariant with respect to the total group of three-dimensional charging symmetries of the heterotic string theory, i.e., to all finite transformations which generate charged solutions from neutral ones and preserve the asymptotics of the starting field configurations. As an application of the presented approach we generate a particular extension of the stationary Einstein–multi-Maxwell theory obtained on the basis of the Kerr–multi-Newman–NUT special class of solutions and establish the conditions under which the resulting multi-dimensional metric of the heterotic string theory is asymptotically flat.