2006/05/05 by Shin'ichirou Yoshida, S. Yoshida, Benjamin C. Bromley +5 · 3 citations
Earth and Planetary Sciences · Physics and Astronomy · #Cosmology and Gravitation Theories #Geophysics and Gravity Measurements #Pulsars and Gravitational Waves Research #gr-qc
paper · pdf · doi:10.1088/0264-9381/23/16/s16
published as Class.Quant.Grav. 23 (2006) S599-S614 · 19 pages, 7 figures. Expanded version of article to be published in Class. Quantum Grav. special issue on Numerical Relativity
arxiv created 2006/05/05 · openalex publication_date 2006/07/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
Results from helically symmetric scalar-field models and first results from a convergent helically symmetric binary neutron-star code are reported here; these are models stationary in the rotating frame of a source with constant angular velocity Ω. In the scalar-field models and the neutron-star code, helical symmetry leads to a system of mixed elliptic–hyperbolic character. The scalar-field models involve nonlinear terms of the form ψ 3 , (∇ψ) 2 and ψ□ψ that mimic nonlinear terms of the Einstein equation. Convergence is strikingly different for different signs of each nonlinear term; it is typically insensitive to the iterative method used, and it improves with an outer boundary in the near zone. In the neutron-star code, one has no control on the sign of the source, and convergence has been achieved only for an outer boundary less than ∼1 wavelength from the source or for a code that imposes helical symmetry only inside a near zone of that size. The inaccuracy of helically symmetric solutions with appropriate boundary conditions should be comparable to the inaccuracy of a waveless formalism that neglects gravitational waves, and the (near zone) solutions we obtain for waveless and helically symmetric BNS codes with the same boundary conditions nearly coincide.