Characteristic Surface Data for the Eikonal Equation

Details Characteristic Surface Data for the Eikonal Equation Characteristic Surface Data for the Eikonal Equation

1998-09-03

arxiv.org/abs/gr-qc/9809016v2

J.Math.Phys. 40 (1999) 1093-1102

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

16 pages, no figures, Scientific Work-Place 2.5, tex, Corrected typos

Scientific paper

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.

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