Cauchy and Goursat problems for the generalized spin zero rest-mass fields on Minkowski spacetime

Peeling of Dirac field on Kerr spacetime

“…We recall some basic formulas on the spin wave operator which act on the spin-1/2 fields on ( BI , g) (for the generalized spin fields see [52,Appendix]). Since the anti-symmetric property of…”

“…In particular, the Goursat problem for the scalar wave equation has solved in the Schwarzschild by Nicolas [34] and the ones for Dirac and Maxwell equations in the Reissner-Nordström-de Sitter spacetime have treated by Mokdad [27,28]. The Goursat prolem for the generalized n/2-spin zero ress-mass equations have studied by the author in [52]. The method combines the vector field method (use the pointwise decays to establish the energy estimates and energy equality) and the generalized results of Hörmander for the scalar and spin wave equations (see [27,28,34,52]).…”

“…The Goursat prolem for the generalized n/2-spin zero ress-mass equations have studied by the author in [52]. The method combines the vector field method (use the pointwise decays to establish the energy estimates and energy equality) and the generalized results of Hörmander for the scalar and spin wave equations (see [27,28,34,52]). The Goursat problem is an important step to construct the conformal scattering theory, i.e, the geometric scattering theory for the field equations in the asymptotic simple and flat spacetimes (in detail see [20,34] for the initial construction of the theory).…”

“…In the present paper, we will extend [52] to establish the conformal scattering theory for the spin-1/2 massless Dirac equation in the Kerr spacetime by using conformal geometric methods. We use the Penrose's conformal mapping on the exterior of Kerr to obtain the domain BI which consits three singular points: the spacelike infinity i 0 and the future (past) timelike infinity i ± .…”

“…We develop the methods in [27,34,50,51,52] to establish the well-posed of the Goursat problem. In particular, the Goursat problem will be solved by using the energy equality and the generalized results of Hörmander in two parts.…”