Abstract: We first study the asymptotic property for some kinds of wave solutions on space-times and introduce the radiation fields as a leading term in the direction of light rays. Then we show the mapping properties from Cauchy data to the radiation fields. From this, we try to solve the wave equations backwards, from null infinity to finite time. 

Reference:

[1] F. G. Friedlander. Radiation fields and hyperbolic scattering theory. Math. Proc. Cambridge Philos. Soc., 88(3):483-515, 1980.

[2] Fang Wang. Radiation eld for Einstein vacuum equations with spacial dimension n>=4. Preprint, ArXiv:1304.0407.