Reissner-Nordstrom in the Bertotti-Robinson-Bonnor-Melvin electromagnetic field

Abstract: The magnetic Reissner-Nordstrom black hole embedded into the Bertotti-Robinson magnetic field is presented. Then it is used, as a seed, to generate, through the Harrison transformation of the Ersnt's equations, the Reissner-Nordstrom metric in the Bertotti-Robinson-Bonnor-Melvin magnetic field. Special cases generalising, the vacuum hairy type I Schwarzschild solution is discussed. The local equivalence between various forms of the Schwarzschild-Bertotti-Robinson is shown by exhibiting the explicit diffeomorphism.