A more general exact solution for the Schwarzschild black hole in a Bertotti-Robinson-Bonnor-Melvin universe

Abstract

We begin by introducing a new parameterization for the Ovcharenko-Podolský family of exact solutions of the Einstein-Maxwell equations describing uncharged and non-accelerating static black holes immersed in an external Bertotti-Robinson electromagnetic field. The new spacetime is, in general, different from the original Ovcharenko-Podolský one, in particular on the branches solving the field equations, for which the original parameterization can lead to black holes with a negative mass, whereas the new one always leads to black holes with a positive mass. Moreover, by introducing additional gauge constants, we remove the various pathologies and ensure consistency with the laws of black hole thermodynamics. We then obtain a new family of Einstein-Maxwell solutions by generalizing this new parameterization, through Harrison transformation within the Ernst method, to also include an external electromagnetic field of the Bonnor-Melvin type. We again identify the appropriate gauge constants required to remove the possible pathologies and ensure that the resulting solutions satisfy the laws of black hole thermodynamics. Finally, we investigate the vacuum subcase of the new family and establish its relation to previously known metrics.