1998/12/09 by Y. Nutku, Nutku, Y.
Engineering · Physics and Astronomy · #Electromagnetic Scattering and Analysis #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Quantum chaos and dynamical systems #Radio Wave Propagation Studies #gr-qc
paper · pdf · doi:10.48550/arxiv.gr-qc/9812030
appeared in "Directions in General Relativity, Papers in honor of Charles Misner" B. L. Hu, M. P. Ryan Jr. and C. V. Vishveshwara editors Cambridge University Press 1993
openalex publication_date 1998/12/09 · arxiv created 1998/12/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The formulation of the Einstein field equations admitting two Killing vectors in terms of harmonic mappings of Riemannian manifolds is a subject in which Charlie Misner has played a pioneering role. We shall consider the hyperbolic case of the Einstein-Maxwell equations admitting two hypersurface orthogonal Killing vectors which physically describes the interaction of two electrovac plane waves. Following Penrose's discussion of the Cauchy problem we shall present the initial data appropriate to this collision problem. We shall also present three different ways in which the Einstein-Maxwell equations for colliding plane wave spacetimes can be recognized as a harmonic map. The goal is to cast the Einstein-Maxwell equations into a form adopted to the initial data for colliding impulsive gravitational and electromagnetic shock waves in such a way that a simple harmonic map will directly yield the metric and the Maxwell potential 1-form of physical interest. For Charles W. Misner on his 60th birthday