Characteristic Surface Data for the Eikonal Equation
General Relativity and Quantum Cosmology
2015-06-25 v2
Abstract
A method of solving the eikonal equation, in either flat or curved space-times, with arbitrary Cauchy data, is extended to the case of data given on a characteristic surface. We find a beautiful relationship between the Cauchy and characteristic data for the same solution, namely they are related by a Legendre transformation. From the resulting solutions, we study and describe their associated wave-front singularities.
Cite
@article{arxiv.gr-qc/9809016,
title = {Characteristic Surface Data for the Eikonal Equation},
author = {Ezra T. Newman and Alejandro Perez},
journal= {arXiv preprint arXiv:gr-qc/9809016},
year = {2015}
}
Comments
16 pages, no figures, Scientific Work-Place 2.5, tex, Corrected typos