Homothetic hyperboloidal coordinates give semilinear wave tails the same exponential decay rate at every compactified radius, removing the late-time resolution bottleneck.
Asymptotics of Schwarzschild black hole perturbations
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abstract
We study linear gravitational perturbations of Schwarzschild spacetime by solving numerically Regge-Wheeler-Zerilli equations in time domain using hyperboloidal surfaces and a compactifying radial coordinate. We stress the importance of including the asymptotic region in the computational domain in studies of gravitational radiation. The hyperboloidal approach should be helpful in a wide range of applications employing black hole perturbation theory.
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Semilinear wave equations in homothetic hyperboloidal coordinates and tail decay
Homothetic hyperboloidal coordinates give semilinear wave tails the same exponential decay rate at every compactified radius, removing the late-time resolution bottleneck.