Insights from Melvin–Kerr–Newman spacetimes

Abstract

Abstract. We examine several aspects of black hole horizon physics using the Melvin-Kerr-Newman (MKN) family of spacetimes. Roughly speaking these are black holes immersed in a distorting background magnetic field and unlike the standard Kerr-Newman (KN) family they are not asymptotically flat. As exact solutions with horizons that can be highly distorted relative to KN, they provide a good testbed for ideas about and theorems constraining black hole horizons.We explicitly show that MKN horizons with fixed magnetic field parameter may be uniquely specified by their area, charge and angular momentum and that the charge and angular momentum are bound by horizon area in the same way as for KN. As expected, extremal MKN horizons are geometrically isomorphic to extremal KN horizons and the geometric distortion of near-extremal horizons is constrained by their proximity to extremality. At the other extreme, Melvin-Schwarzschild (MS) solutions may be infinitely distorted, however for intermediate cases any non-zero charge or angular momentum restricts distortions to be finite. These properties are in agreement with known theorems but are seen to be satisfied in interesting and non-trivial ways.

Black hole thermodynamics with conical defects

“…Given the central importance of black hole thermodynamics in theoretical gravity, it is surprising that until recently only the thermodynamics of relatively simply systems had been explored. Although our catalog of exact black hole solutions is limited (mostly) to isolated gravitating systems, there is a class of intriguing exceptions, given by axisymmetric solutions to the Einstein equations [12,13], including axisymmetric multiple black holes [14][15][16][17][18], black holes in magnetic flux tubes (including a study of thermodynamics) [19][20][21], and most pertinently for our discussion, the accelerating black hole. This last example has an exact solution known as the C-metric [22,23], corresponding to a black hole with a conical deficit emerging from one pole, or unequal conical deficits emerging from each pole.…”

Mass of Kerr-Newman black holes in an external magnetic field

“…While several relevant features of this solution have been disclosed since its publication, some aspects of the Ernst-Wild solution, concerning the energy and thermodynamics, still remain controversial due to the unconventional asymptotic region. In the last years, several attempts have been made in that direction by using different theoretical methods, but still there is no general agreement; see, for instance, [10,[14][15][16][17][18][19].…”

Extremal black holes in strong magnetic fields: Near-horizon geometries and Meissner effect

“…It was fully developed in 2015 8,9 , where it was further discussed that this fact can be also inferred using certain uniqueness theorems like the one of Lewandowski and Pawlowski 10 . Furthermore, it is remarkable that when we define the angular momentum of extremal MKN black holes byĴ =âM , i.e.…”