1999/04/05 by J. T. Whelan, John T. Whelan, Whelan, John T.
Mathematics · Physics and Astronomy · #Astrophysics #Binary number #Boundary (topology) #Classical mechanics #Consistency (knowledge bases) #Cosmology and Gravitation Theories #Einstein #Einstein field equations #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #General relativity #Geometry #Gravitation #Gravitational energy #Gravitational wave #Mathematical analysis #Mathematics #Physics #Pulsars and Gravitational Waves Research #Quantum mechanics #Relativity and Gravitational Theory #Spacetime #Symmetry (geometry) #Theoretical physics #gr-qc
paper · pdf · doi:10.48550/arxiv.gr-qc/9904010
published in arXiv (Cornell University) (Cornell University) · 9 pages, LaTex with texas.sty style file (included), 3 figures included via epsfig, submitted to the Proceedings of the 19th Texas Symposium (Paris, December 1998)
arxiv created 1999/04/05 · openalex publication_date 1999/04/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
I describe the current status of a collaboration with J.D. Romano, R.H. Price, and W. Krivan to model the geometry of and gravitational radiation emitted by a binary system of compact objects in the regime where non-perturbative gravitational effects exist, but the rate of inspiral is still small relative to the orbital frequency. The method of looking for a stationary spacetime which approximates the evolving solution is initially being tested on a simpler model with an additional translational symmetry. This report consists of a general description of the method, followed by summaries of three techniques in varying stages of development: the simplification of the Einstein equations in the presence of two commuting Killing vectors which form a non-orthogonally-transitive symmetry group, the boundary conditions appropriate to the balance of ingoing and outgoing radiation needed to reconcile a stationary radiating solution with conservation of energy, and the treatment of gravitational waves far from the sources as linearized perturbations to the Levi-Civita spacetime. The poster presentation with which this paper is associated is available on line at http://www-itp.unibe.ch/~whelan/poster.ps.gz and the current status of the project is described at http://www-itp.unibe.ch/~whelan/qsbi.html