2012/12/12 by David Hilditch, Sebastiano Bernuzzi, Marcus Thierfelder +4 · 2 citations
Mathematics · Physics and Astronomy · #Amplitude #Astrophysical Phenomena and Observations #Binary number #Boundary (topology) #Boundary value problem #Classical mechanics #Gamma-ray bursts and supernovae #General relativity #Gravitation #Gravitational wave #Hamiltonian (control theory) #Mathematical analysis #Mathematics #Neutron star #Numerical relativity #Physics #Pulsars and Gravitational Waves Research #Quantum mechanics #Spurious relationship #gr-qc
paper · pdf · doi:10.1103/physrevd.88.084057
published as Phys. Rev. D 88, 084057 (2013)
arxiv created 2012/12/12 · openalex publication_date 2013/10/30 · arxiv updated 2013/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Numerical relativity simulations of compact binaries with the Z4c and Baumgarte-Shapiro-Shibata-Nakamura-Oohara-Kojima (BSSNOK) formulations are compared. The Z4c formulation is advantageous in every case considered. In simulations of nonvacuum spacetimes, the constraint violations due to truncation errors are between 1 and 3 orders of magnitude lower in the Z4c evolutions. Improvements are also found in the accuracy of the computed gravitational radiation. For equal-mass irrotational binary neutron star evolutions, we find that the absolute errors in phase and amplitude of the waveforms can be up to a factor of 4 smaller. The quality of the Z4c numerical data is also demonstrated by a remarkably accurate computation of the Arnowitt-Deser-Misner mass from surface integrals. For equal-mass nonspinning binary puncture black hole evolutions, we find that the absolute errors in phase and amplitude of the waveforms can be up to a factor of 2 smaller. In the same evolutions, we find that away from the punctures the Hamiltonian constraint violation is reduced by between 1 and 2 orders of magnitude. Furthermore, the utility of gravitational radiation controlling, constraint preserving boundary conditions for the Z4c formulation is demonstrated. The evolution of spacetimes containing a single compact object confirms earlier results in spherical symmetry. The boundary conditions avoid spurious and nonconvergent effects present in high resolution runs with either formulation with a more naive boundary treatment. We conclude that Z4c is preferable to BSSNOK for the numerical solution of the 3+1 Einstein equations with the puncture gauge.