Null foliations for scattering problems

Abstract

We study conformal scattering problems with null foliations. The Goursat problem of the scalar wave equation in Minkowski spacetime is numerically solved in compactified double-null coordinates. Stable numerical evolution is achieved by integration stencils along characteristics. We obtain second-order convergent results, except for first-order convergence on future null infinity $\mathcal{I}^+$ induced by the singular spatial infinity $i^0$ for multipole numbers $\ell \ge 2$. Richardson extrapolation can remedy this deterioration, enhancing the convergence rate to approximately 1.5. Our method accurately computes the scattering matrix, e.g., phase shifts sourced by a Pöschl-Teller potential, and successfully captures the self-defocusing Kerr effect for the semi-linear wave equation. I will also present results on the conformal scattering problem of the Regge-Wheeler equation in Schwarzschild spacetime.