Construction of initial data for 3+1 numerical relativity

2007/04/30 by Eric Gourgoulhon, Éric Gourgoulhon
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Applied mathematics #Black Holes and Theoretical Physics #Computer science #Conformal map #Constraint (computer-aided design) #General relativity #Geometry #Geophysics and Gravity Measurements #Mathematical analysis #Mathematics #Numerical relativity #Physics #Pulsars and Gravitational Waves Research #Simple (philosophy) #Theoretical physics #Theory of relativity #gr-qc

paper · pdf · doi:10.1088/1742-6596/91/1/012001

published as J.Phys.Conf.Ser.91:012001,2007 · Minor modifications, updated references, 28 pages, 5 figures, contribution to the Proceedings of the VII Mexican School on Gravitation and Mathematical Physics, held in Playa del Carmen, Mexico (Nov. 26 - Dec. 2, 2006), Journal of Physics: Conference Series, in press

openalex publication_date 2007/11/01 · arxiv created 2007/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

This lecture is devoted to the problem of computing initial data for the Cauchy problem of 3+1 general relativity. The main task is to solve the constraint equations. The conformal technique, introduced by Lichnerowicz and enhanced by York, is presented. Two standard methods, the conformal transverse-traceless one and the conformal thin sandwich, are discussed and illustrated by some simple examples. Finally a short review regarding initial data for binary systems (black holes and neutron stars) is given.

Citations

• Gravitational-Wave Extraction from an Inspiraling Configuration of Merging Black Holes
• Numerical method for binary black hole/neutron star initial data: Code test
• Binary Neutron Stars in General Relativity: Quasi-Equilibrium Models
• Spin-orbit interactions in black-hole binaries
• Periodic solutions of the Einstein equations for binary systems
• Binary black hole initial data for numerical general relativity based on post-Newtonian data
• A multi-domain spectral method for initial data of arbitrary binaries in general relativity
• Black-hole puncture initial data with realistic gravitational wave content
• Circular orbits and spin in black-hole initial data
• Effective one-body approach to general relativistic two-body dynamics
• Binary black hole merger dynamics and waveforms
• The initial value problem in numerical relativity
• Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries
• Relativistic neutron star merger simulations with non-zero temperature equations of state