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Characteristic Surface Data for the Eikonal Equation

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.

preprint1998arXivOpen access
Ezra T. NewmanAlejandro Perez
gr-qc
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Open access2 authors1 topic
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Ezra T. NewmanAlejandro Perez

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