Homothetic hyperboloidal coordinates give semilinear wave tails the same exponential decay rate at every compactified radius, removing the late-time resolution bottleneck.
What does a strongly excited 't Hooft-Polyakov magnetic monopole do?
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abstract
The time evolution of strongly exited SU(2) Bogomolny-Prasad-Sommerfield (BPS) magnetic monopoles in Minkowski spacetime is investigated by means of numerical simulations based on the technique of conformal compactification and on the use of hyperboloidal initial value problem. It is found that an initially static monopole does not radiate the entire energy of the exciting pulse toward future null infinity. Rather, a long-lasting quasi-stable `breathing state' develops in the central region and certain expanding shell structures -- built up by very high frequency oscillations -- are formed in the far away region.
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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.