Lightlike Hypersurfaces And Electromagnetism
In this Chapter we apply some results of Chapters 4 and 7 to study a class of lightlike hypersurfaces M of 4-dimensional electromagnetic spacetimes. Section 8.1 deals with the needed basic information on Minkowski spacetime. In section 8.2, we study a class of invariant lightlike hypersurfaces having induced non-singular and singular electromagnetic tensor fields denoted by F. We show that F on M exists if and only if M is totally geodesic. Section 8.3 deals with some geometric properties of (1,1) tensor fields (associated to F) satisfying an algebraic cubic equation. We show that a class of electromagnetic invariant lightlike hypersurfaces comes from the physically significant homogeneous spacetime manifolds of general relativity.
KeywordsMaxwell Equation Tensor Field Minkowski Spacetime Spacetime Manifold Connection Versus
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