Integral Formula for the Characteristic Cauchy Problem on a curved Background

Jérémie Joudioux (1)

1 LM-Brest - Laboratoire de Mathématiques

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.

Mots clés: Goursat problem; Dirac equation; Newman-Penrose formalism

Domaines: Equations aux dérivées partielles [math.AP]; Géométrie différentielle [math.DG]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Jérémie Joudioux. Integral Formula for the Characteristic Cauchy Problem on a curved Background. 2009. ⟨hal-00426219⟩