A hyperboloidal study of tail decay rates for scalar and Yang-Mills fields

Abstract

We investigate the asymptotic behavior of spherically symmetric solutions to scalar wave and Yang-Mills equations on a Schwarzschild background. The studies demonstrate the astrophysical relevance of null infinity in predicting radiation signals for gravitational wave detectors and show how test fields on unbounded domains in black hole spacetimes can be simulated conveniently by numerically solving hyperboloidal initial value problems.

8 pages, 7 figures

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• Spacelike matching to null infinity
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• Gravitational perturbations of Schwarzschild spacetime at null infinity and the hyperboloidal initial value problem
• Asymptotics of Schwarzschild black hole perturbations
• Intermediate behavior of Kerr tails
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• Hyperboloidal Approach to Quasinormal Modes
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• A GPU-accelerated mixed-precision WENO method for extremal black hole and gravitational wave physics computations
• Saddle-point dynamics of a Yang-Mills field on the exterior Schwarzschild spacetime
• Global simulations of Minkowski space-time including space-like infinity
• Formation and decay of Einstein-Yang-Mills black holes
• Unconstrained hyperboloidal evolution of black holes in spherical symmetry with GBSSN and Z4c
• Evolution of a mass-less test scalar field on Boson Stars space-times
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• Wave maps on a wormhole
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• Sine-Gordon on a wormhole
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• Hyperboloidal method for frequency-domain self-force calculations
• A hyperboloidal method for numerical simulations of multidimensional nonlinear wave equations: nonlinear tails