Fully relativistic three-dimensional Cauchy-characteristic matching

Sizheng Ma, Jordan Moxon, Mark A. Scheel, Kyle C. Nelli, Nils Deppe, Marceline S. Bonilla, Lawrence E. Kidder, Prayush Kumar, Geoffrey Lovelace, William Throwe, Nils L. Vu
General Relativity and Quantum Cosmology, General Relativity and Quantum Cosmology (gr-qc)
2023-08-19 16:00:00
A fully relativistic three-dimensional Cauchy-characteristic matching (CCM) algorithm is implemented in a numerical relativity code SpECTRE. The method is free of approximations and can be applied to any physical system. We test the algorithm with various scenarios, including the propagation of Teukolsky waves within a flat background, the perturbation of a Kerr black hole with a Teukolsky wave, and the injection of a gravitational-wave pulse from the characteristic grid. Our investigations reveal no numerical instabilities in the simulations. In addition, the tests indicate that the CCM algorithm effectively directs characteristic information into the inner Cauchy system, yielding higher precision in waveforms and smaller violations of Bondi-gauge constraints, especially when the outer boundary of the Cauchy evolution is at a smaller radius.
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