Schwarzschild spacetime immersed in test nonlinear electromagnetic fields

TL;DR

This paper extends Wald's solution for Kerr black holes in magnetic fields to nonlinear electromagnetic theories, providing perturbative corrections in Euler–Heisenberg and Born–Infeld models, and discusses implications for highly conducting stars.

Contribution

It introduces a perturbative method to generalize Wald's solution for Schwarzschild spacetime in nonlinear electromagnetic theories, specifically Euler–Heisenberg and Born–Infeld.

Findings

Derived lowest order corrections to Wald's solution in nonlinear models

Applied perturbative approach to Schwarzschild spacetime

Discussed implications for highly conducting stars in magnetic fields

Abstract

Kerr black hole immersed in test, asymptotically homogeneous magnetic field, aligned along the symmetry axis, is described by Wald's solution. We show how the static case of this solution may be generalized for nonlinear electromagnetic models via perturbative approach. Using this technique we find the lowest order correction to Wald's solution on Schwarzschild spacetime in Euler--Heisenberg and Born--Infeld theories. Finally, we discuss the problem of highly conducting star in asymptotically homogeneous magnetic field.