Einstein-Maxwell Black Hole Solutions

In contrast to the five-dimensional Einstein equations in vacuum, the stationary and axisymmetric Einstein-Maxwell equations do not correspond to an integrable system in the general case. As a result, systematic generation of exact solutions is only possible in certain integrable subclasses which possess additional symmetries. In this chapter we describe such cases and construct explicitly some of the Einstein-Maxwell black hole solutions which belong to them using the action of hidden symmetry group or applying Bäcklund transformations. As in the previous chapters we focus on asymptotically flat spacetimes.