CAUCHY-CHARACTERISTIC EVOLUTION OF EINSTEIN-KLEIN-GORDON SYSTEMS - THE BLACK-HOLE REGIME

The Cauchy+characteristic matching (CCM) problem for the scalar wave e quation is investigated in the background geometry of a Schwarzschild black hole. Previously reported work developed the CCM framework for t he coupled Einstein-Klein-Gordon system of equations, assuming a regul ar center of symmetry. Here, the time evolution after the formation of a black hole is pursued, using a CCM formulation of the governing equ ations perturbed around the Schwarzschild background. An extension of the matching scheme allows for arbitrary matching boundary motion acro ss the coordinate grid. As a proof of concept, the late time behavior of the dynamics of the scalar field is explored. The power-law tails i n both the timelike and null infinity limits are verified.