Black hole perturbation theory in a light cone gauge
The metric of a Schwarzschild black hole immersed in a uniform magnetic field is studied using black hole perturbation theory in a light crone coordinate system that penetrates the event horizon and possesses a clear geometrical meaning. The magnetic field, which is distorted due to the presence of the black hole, has strength 'B' which is assumed to be small compared to the curvature of the spacetime which allows the perturbed metric to be calculated to order 'B'2 only. The coordinates allow for an easy identification of the event horizon and the properties of the perturbed black hole are studied. To interpret this perturbed metric, the advanced coordinates are decomposed into irreducible parts which yields the metric of a perturbed black hole in the limit 'r' >> 2'M'. Finally we compare our perturbed solution to an exact solution. We show that our perturbed solution is able to match the exact solution but has the freedom to describe a larger class of physically relevant solutions.