Schwarzschild black hole perturbed by a force-free magnetic field

TL;DR

This paper investigates how a force-free magnetic field influences the structure of a Schwarzschild black hole, revealing modifications to the metric and a transition from static to stationary spacetime.

Contribution

It models the perturbation of a Schwarzschild black hole by a force-free magnetic field, showing changes in the metric including off-diagonal elements and a static to stationary transition.

Findings

Modification of diagonal metric elements due to magnetic field

Emergence of off-diagonal metric components

Transition from static to stationary spacetime

Abstract

We envisage a black hole perturbed by a force-free magnetic field (FFMF) outside and attempt to determine its structure. We suppose the metric that describes this black hole is of the static spherical type, that is Schwarzschild, and the energy-momentum tensor emanating from an FFMF source perturbs this background metric, in this regard one can imagine a magnetic accretion disk around the black hole. By solving the equations for such a configuration, we will show that in addition to modifying the diagonal elements of the background metric, we will also see the non-zeroing of the off-diagonal elements of the general metric, one of the immediate consequences of which will be a static to stationary transition. "Space-time tells matter how to move; matter tells space-time how to curve" -- John Archibald Wheeler