General Relativity

Abstract

* Dedicated to Carl Ludwig Siegel in Gottingen on his sixtieth birthday. t A detailed paper will appear in Comm. Pure and Appl. Math. The laws of propagation of (liscontinuities along bicharacteristics, in particular for differential equations of second order, have often been discussed in the literature. (See, e.g., R. Courant and D. Hilbert, Methods of Mathematical Physics, Vol. II, chaps. V, VI, and J. B. Keller, "Geometrical Acoustics I. The Theory of Weak Shock Waves," J. Appl. Phys., 25, 938-947, 1954.) 1 See K. 0. Friedrichs, Comm. Pure and Appl. Math., 7, 345-393, 1954, for symmetric hyperbolic systems, and J. Leray, Lectures on Hyperbolic Equations with Variable Coefficients (Princeton, N.J.: Institute for Advanced Study, 1952), for general hyperbolic systems. 2 Radon's formula was used in the solution of Cauchy's problem for equations with constant coefficients by R. Courant and A. Lax, Comm. Pure and Appl. Math., Vol. 8, 1955. For diverse application see Fritz John, Plane Waves and Spherical Means (New York: Interscience Publishers, Inc., 1956).