Waveequation integrals in a spacetime with the metric of a gravitational plane wave
Abstract
General analytical solutions to the scalar wave equation and the (spinor) Maxwell equations on the metric background of a weak gravitational plane wave are obtained on the basis of a previously determined integral equation that is equivalent to the wave equation with variable coefficients. These solutions are presented in the form of a generalized retarded potential or a generalized Kirchhoff formula plus a surface integral. An equation for the light cone corresponding to the moving surface of the wave front is derived along with an expression for the relevant Sobolev function. Different forms of the lightcone equation and the invariance of the Sobolev function are examined.
 Publication:

Eesti NSV Teaduste Akadeemia Toimetised Fuusika Matemaatika
 Pub Date:
 1978
 Bibcode:
 1978ETATF..27..132U
 Keywords:

 Gravitational Waves;
 Maxwell Equation;
 SpaceTime Functions;
 Wave Equations;
 Electric Fields;
 Huygens Principle;
 LightCone Expansion;
 Magnetic Fields;
 Minkowski Space;
 Astrophysics