Characteristic Surface Data for the Eikonal Equation
arXiv:gr-qc/9809016 · doi:10.1063/1.532708
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.
16 pages, no figures, Scientific Work-Place 2.5, tex, Corrected typos