In this paper, we establish a conformal scattering theory for defocusing semilinear wave equations on Schwarzschild spacetime. We combine the energy and pointwise decay results for solutions obtained in [19] with a Sobolev embedding on spacelike hypersurfaces to derive two-sided energy estimates between the energy flux of solutions through the Cauchy initial hypersurface \(\Sigma _0 = \{ t = 0 \}\) and that through the null conformal boundaries \(\mathfrak {H}^+ \cup {\mathscr {I}}^+\) (respectively, \(\mathfrak {H}^- \cup {\mathscr {I}}^-\) ). By combining these estimates with the well-posedness of the Cauchy and Goursat problems for nonlinear wave equations, we construct a bounded linear and locally Lipschitz scattering operator that maps past scattering data to future scattering data.
