Insights from Melvin-Kerr-Newman spacetimes

TL;DR

This paper explores the properties of black hole horizons in Melvin-Kerr-Newman spacetimes, revealing how their geometry and physical parameters relate, especially under distortion and extremality conditions, providing insights into horizon theorems.

Contribution

It demonstrates that MKN horizons can be uniquely characterized by area, charge, and angular momentum, and analyzes how distortions relate to extremality and physical bounds.

Findings

MKN horizons are uniquely specified by area, charge, and angular momentum.

Extremal MKN horizons are geometrically identical to extremal KN horizons.

Distortions are constrained by extremality and physical bounds.

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.