Colliding plane waves in general relativity
The collision and non-linear interaction of plane waves in Einstein's general theory of relativity has received considerable attention in recent years. Initially, it was widely thought that such collisions inevitable produce curvature singularities. More recently, however, a surprisingly rich structure of such space-times has been discovered. This volume presents a unified and comprehensive survey to the current research in this topic which will be suitable for graduate students and research workers whose research lies in general relativity. The first eight chapters present the background to the subject, introduce the field equations, and include a discussion of some qualitative aspects of their solution. A detailed account is included of the Kahn-Penrose solution since it exhibits the general character of most colliding plane wave solutions. The latter half of the book is devoted to a catalogue of further exact solutions describing the collision of both gravitational and electromagnetic plane waves. This includes a discussion of the significance of known solutions and a summary of topics of current research interest. As a result, the book will serve both as an invaluable research reference and also as the means to teach and study this active area of research in general relativity.
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COLLIDING IMPULSIVE GRAVITATIONAL WAVES
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2dudv aligned approaching waves appropriate arbitrary constants Bell-Szekeres solution boundary conditions Cauchy horizon Chandrasekhar and Xanthopoulos class of solutions colinear colliding electromagnetic waves colliding plane waves colliding wave collision of plane considered contain convenient coordinate singularity cos2 cosh cosh2 curvature singularity curvature tensor described in Section describes the collision Einstein's electromagnetic field electromagnetic waves Ernst equation Ernst potential exact solutions expressed flat focusing geodesic gravitational field hypersurface impulsive gravitational waves impulsive waves initial data interaction region junction conditions Kasner Kerr solution Khan-Penrose solution Killing vectors line element line element 6.20 linear main field equations metric functions neutrino fields non-linear null coordinates obtained parameters plane gravitational waves plane wave solutions polarization possible region IV Ricci tensor satisfied seen shown sin2 singularity in region singularity structure sinh solitons solution described solution given space-like space-time Szekeres solution techniques theorem tion vacuum solution wave components wave front Weyl tensor Yurtsever zero