Abstract
AbstractThe results of a previous paper are applied to a study of the class of Kerr–Schild metrics in general relativity. These metrics have the formwhere η is the flat (Minkowski) space-time metric, m is an arbitrary real number, and 1 is a null covector. It is already known that for a certain restricted subclass of these metrics, the vacuum Einstein field equations, viz.can be written in the formwhere γ is a complex potential. Using the methods developed in a previous paper, such space-times are characterized by means of a special family of complex surfaces in three-dimensional Euclidean space, and the exact solutions for the metric g are consequently recovered. It is also shown that the field equations for a much wider class of Kerr–Schild metrics can be expressed in terms of a potential formalism, not only in the vacuum case, but also for many electrovacuum solutions.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
