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Well-Posed Initial-Boundary Evolution in General Relativity

Bela Szilagyi·Jeffrey Winicour
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Abstract

Maximally dissipative boundary conditions are applied to the initial-boundary value problem for Einstein's equations in harmonic coordinates to show that it is well-posed for homogeneous boundary data and for boundary data that is small in a linearized sense. The method is implemented as a nonlinear evolution code which satisfies convergence tests in the nonlinear regime and is robustly stable in the weak field regime. A linearized version has been stably matched to a characteristic code to compute the gravitational waveform radiated to infinity.

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Bela Szilagyi, Jeffrey Winicour. 2003-06-19. Well-Posed Initial-Boundary Evolution in General Relativity. https://doi.org/10.1103/physrevd.68.041501

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