Abstract
We study stationary black holes in the presence of an external strong magnetic field. In the case where the gravitational backreaction of the magnetic field is taken into account, such an scenario is well described by the Ernst-Wild solution to Einstein-Maxwell field equations, representing a charged, stationary black hole immersed in a Melvin magnetic universe. This solution, however, describes a physical situation only in the region close to the black hole. This is due to the following two reasons: Firstly, Melvin spacetime is not asymptotically locally flat; secondly, the non-static Ernst-Wild solution is not even asymptotically Melvin due to the infinite extension of its ergoregion. All this might seem to be an obstruction to address an scenario like this; for instance, it seems to be an obstruction to compute conserved charges as this usually requires a clear notion of asymptotia. Here, we circumvent this obstruction by providing a method to compute the conserved charges of such a black hole by restricting the analysis to the near horizon region. We compute the Wald entropy, the mass, the electric charge, and the angular momentum of stationary black holes in highly magnetized environments from the horizon perspective, finding results in complete agreement with other formalisms.
Highlights
Compact objects in strong magnetic fields are of great importance in astrophysics
We will study the case of black holes placed in a region of very strong magnetic fields, including the gravitational backreaction of the latter on the spacetime geometry
The solution, describes a physical situation as long as one focuses on the region close to the black hole. This is due to the nonstandard asymptotics of the Melvin spacetime, which is not asymptotically flat; in addition, as shown in [11], Ernst-Wild solution is not strictly asymptotically Melvin due to the infinite extension of its ergoregion. All this might seem to represent an obstruction to address an scenario like this, as in gravitational theories one frequently deals with computations that demand to have a clear notion of asymptotia, an example being the standard methods to compute conserved charges
Summary
Compact objects in strong magnetic fields are of great importance in astrophysics. Scenarios such as supermassive black holes in active galactic nuclei, or even at the center of our galaxy [1] could be of that sort. The solution, describes a physical situation as long as one focuses on the region close to the black hole This is due to the nonstandard asymptotics of the Melvin spacetime, which is not asymptotically flat; in addition, as shown in [11], Ernst-Wild solution is not strictly asymptotically Melvin due to the infinite extension of its ergoregion. IV, we will extend the analysis to the case of electrically charged, stationary black hole solutions immersed in a strong external magnetic field This shows that this case admits a near horizon description as the one in [12], yielding supertranslations and superrotation charges. VI, we briefly discuss the case of magnetically charged black holes in an external field
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