Fourth-post-Newtonian exact approximation to general relativity

2010/02/28 by David Brizuela, Gerhard Schäfer, Gerhard Schaefer · 4 citations
Medicine · Physics and Astronomy · #Black Holes and Theoretical Physics #Calculus (dental) #Classical mechanics #Cosmology and Gravitation Theories #General relativity #Mathematical physics #Medicine #Newtonian fluid #Physics #Pulsars and Gravitational Waves Research #Theoretical physics #Theory of relativity #gr-qc

paper · pdf · doi:10.1103/physrevd.81.084014

published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 81(8) (American Physical Society) · Replaced by the published version. Some clarifications and references added.

openalex publication_date 2010/04/06 · arxiv created 2010/04/12 · arxiv updated 2010/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

An approximation to general relativity is presented that agrees with the Einstein field equations up to and including the fourth post-Newtonian (PN) order. This approximation is formulated in a fully constrained scheme: all involved equations are explicitly elliptic except the wave equation that describes the two independent degrees of freedom of the gravitational field. The formalism covers naturally the conformal-flat condition approach by Isenberg, Wilson, and Mathews and the improved second PN-order exact approach conformal-flat condition plus. For stationary configurations, like Kerr black holes, agreement with general relativity is achieved even through 5PN order. In addition, a particularly interesting 2PN-exact waveless approximation is analyzed in detail, which results from imposing more restrictive conditions. The proposed scheme can be considered as a further development on the waveless approach suggested by Sch"afer and Gopakumar [26].

Citations

• Mathematical issues in a fully constrained formulation of the Einstein equations
• Models of helically symmetric binary systems
• Periodic solutions of the Einstein equations for binary systems
• WAVELESS APPROXIMATION THEORIES OF GRAVITY
• Binary black hole initial data for numerical general relativity based on post-Newtonian data
• Binary black hole coalescence in semianalytic puncture evolution
• Black-hole puncture initial data with realistic gravitational wave content
• Skeleton approximate solution of the Einstein field equations for multiple black-hole systems
• Post-Newtonian initial data with waves: progress in evolution
• Republication of: The dynamics of general relativity
• Constrained scheme for the Einstein equations based on the Dirac gauge and spherical coordinates
• Minimal no-radiation approximation to Einstein’s field equations
• Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries