Derives a provably stable 3D SBP scheme for linear waves on hyperboloidal slices using compactification, rescaling, and abstract dissipation in spherical polar coordinates.
Hyperboloidal evolution with the Einstein equations
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abstract
We consider an approach to the hyperboloidal evolution problem based on the Einstein equations written for a rescaled metric. It is shown that a conformal scale factor can be freely prescribed a priori in terms of coordinates in a well-posed hyperboloidal initial value problem such that the location of null infinity is independent of the time coordinate. With an appropriate choice of a single gauge source function each of the formally singular conformal source terms in the equations attains a regular limit at null infinity. The suggested approach could be beneficial in numerical relativity for both wave extraction and outer boundary treatment.
fields
gr-qc 2years
2026 2representative citing papers
Exact conformal matching of three compactified regions enables global time-domain evolution of scalar waves from past to future null infinity in Minkowski space without artificial timelike boundaries.
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Hyperboloidal evolution for scalar scattering in Minkowski space
Exact conformal matching of three compactified regions enables global time-domain evolution of scalar waves from past to future null infinity in Minkowski space without artificial timelike boundaries.