2006/07/31 by Mark Scheel, Mark A. Scheel, Harald P. Pfeiffer +5 · 222 citations
Mathematics · Physics and Astronomy · #Applied mathematics #Art #Black Holes and Theoretical Physics #Computer science #Cosmology and Gravitation Theories #Dual (grammatical number) #Einstein #Literature #Mathematical physics #Mathematics #Physics #Pulsars and Gravitational Waves Research #gr-qc
paper · pdf · doi:10.1103/physrevd.74.104006
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 74(10) (American Physical Society) · Updated to agree with published version
openalex publication_date 2006/11/02 · arxiv created 2007/12/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A method is introduced for solving Einstein's equations using two distinct coordinate systems. The coordinate basis vectors associated with one system are used to project out components of the metric and other fields, in analogy with the way fields are projected onto an orthonormal tetrad basis. These field components are then determined as functions of a second independent coordinate system. The transformation to the second coordinate system can be thought of as a mapping from the original inertial coordinate system to the computational domain. This dual-coordinate method is used to perform stable numerical evolutions of a black-hole spacetime using the generalized harmonic form of Einstein's equations in coordinates that rotate with respect to the inertial frame at infinity; such evolutions are found to be generically unstable using a single rotating-coordinate frame. The dual-coordinate method is also used here to evolve binary black-hole spacetimes for several orbits. The great flexibility of this method allows comoving coordinates to be adjusted with a feedback control system that keeps the excision boundaries of the holes within their respective apparent horizons.