Integral Formula for the Characteristic Cauchy Problem on a curved Background

Details Integral Formula for the Characteristic Cauchy Problem on a curved Background Integral Formula for the Characteristic Cauchy Problem on a curved Background

2009-10-24

arxiv.org/abs/0910.4620v1

Mathematics

Analysis of PDEs

42 pages

Scientific paper

We give a local integral formula, valid on general curved space-times, for the characteristic Cauchy problem for the Dirac equation with arbitrary spin using the method developed by Friedlander in his book "the wave equation on a curved spacetime" (1975). The results obtained by Penrose in the flat case in "Null hypersurface initial data for classical fields of arbitrary spin for general relativity" (Gen. Rel. Grav 1980) are recovered directly. It is expected that this method can be used to obtain sharp estimates for the characteristic Cauchy problem for the Dirac equation.

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