Conformal Scattering Theory for the Dirac Equation on Kerr Spacetime

Conformal scattering theories for tensorial wave equations on Schwarzschild spacetime

“…in Schwarzschild background. To avoid the singularities at i + and i 0 , we use the same method as in appendix B in [59,63,65]. In particular, we take S which is a spacelike hypersurface on M whose intersection with the horizon is the crossing sphere and which crosses I + strictly in the past of the support of the data.…”

“…Remark 6. The Goursat problems for wave equations on spinor fields were also established in some other works [53,54,64,65].…”

“…This fact leads to the complication of the case of Kerr spacetime. In a recent work [65], we have established the conformal scattering theory for the massless Dirac equation on Kerr spacetime, where it remains to have a conserved current for the equation. This work can be useful for the construction of conformal scattering theories on Kerr spacetime for the scalar wave, tensorial wave and Maxwell equations.…”

“…In particular, the conformal scattering theory (i.e. the geometric scattering theory) has been studied extensively from the early works by Friedlander [25][26][27][28][29], Baez et al [8], Hörmander [37] to recent ones by Mason and Nicolas [49], Joudioux [41,42], Nicolas [59], Mokdad [53,54], Taujanskas [72] and Pham [63,65].…”

“…This is the first step to obtain the conformal scattering theory for the linearized gravity fields on the Schwarzschild spacetime which is spherical symmetric. The extension of the conformal scattering theory on Kerr spacetime (which is non-static and non-spherical symmetric) has been established recently by Pham [65] for the massless Dirac equations. In the works on the exterior domains of black hole spacetimes [53,63,65], the authors used the results about the uniformly bounded energy, Morawertz estimate and pointwise decay of the fields to establish the energy identity up to the future (resp.…”