Schwarzschild black hole immersed in a homogeneous electromagnetic field

An exact and simple enough solution of the Einstein-Maxwell field equations is presented. This electrovacuum static axisymmetric solution possesses a clear physical interpretation: it is an external field of nonrotating uncharged mass immersed in homogeneous external electromagnetic and gravitational fields-the Bertotti-Robinson universe. Unlike the well known Ernst solution for a black hole in the Melvin universe, in our solution the black hole is immersed in a space-time with a completely spatially homogeneous magnetic (or electric) field and with a different (R(2) X S-2) topology. The influence of this specific background space-time topology, the structure of curvature singularities, the relation between the laws of motion, and the condition of the absence of any unphysical non-curvature singularities as well as some other questions are considered. A brief sketch of the solution construction method used here and of its various applications, a comparison with other methods, as well as a general discussion concerning the construction of solutions for interacting fields are presented in the Appendix.