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The Cauchy+characteristic matching (CCM) problem for the scalar wave equationis investigated in the background geometry of a Schwarzschild black hole.Previously reported work developed the CCM framework for the coupledEinstein-Klein-Gordon system of equations, assuming a regular center ofsymmetry. Here, the time evolution after the formation of a black hole ispursued, using a CCM formulation of the governing equations perturbed aroundthe Schwarzschild background. An extension of the matching scheme allows forarbitrary matching boundary motion across the coordinate grid. As a proof ofconcept, the late time behavior of the dynamics of the scalar field isexplored. The power-law tails in both the time-like and null infinity limitsare verified.

Cauchy-characteristic evolution of Einstein-Klein-Gordon systems: The black hole regime