Schwarzschild Black Hole in Uniform Magnetic Field in Einstein-Maxwell-Dilaton Theories

We obtain the Kerr black hole in an external uniform magnetic field in the Kaluza-Klein (KK) theory via a standard solution-generating technique. Using this as our starting point, we construct exact static solutions describing a Schwarzschild black hole immersed in the external uniform magnetic field in general string-inspired Einstein-Maxwell-dilaton (EMD) theories, thereby embedding the static Kerr-Bertotti-Robinson (KBR) solution into the general framework of EMD theories. We also construct electrovacuum solutions involving both electric and magnetic fields in EMD theories and generalize the system to include mutltiple Maxwell fields and dilatons. These equations of motion can be reduced to Toda-like equations, allowing us to obtain analytic electrovacua associated with Toda equations of all rank-2 Lie groups. We further construct exact solutions of a Schwarzschild black hole immersed in these electrovacua.