2014/04/30 by Clifford M. Will, Clifford M Will · 1 citation
Physics and Astronomy · #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Component (thermodynamics) #Conserved quantity #Equations of motion #Motion (physics) #Newtonian fluid #Precession #Pulsars and Gravitational Waves Research #Relativistic particle #Relativistic quantum chemistry #astro-ph.GA #gr-qc
paper · pdf · doi:10.1088/0264-9381/31/24/244001
published as Classical and Quantum Gravity 31, 244001 (2014) · 10 pages, submitted to Classical and Quantum Gravity for a focus issue on Galactic Centers
arxiv created 2014/04/30 · openalex publication_date 2014/12/01 · arxiv updated 2016/04/07 · openalex created_date 2016/09/16 · openalex updated_date 2026/08/05
Conventional approaches to incorporating general relativistic effects into the dynamics of N-body systems containing central black holes, or of hierarchical triple systems with a relativistic inner binary, may not be adequate when the goal is to study the evolution of the system over a timescale related to relativistic secular effects, such as the precession of the pericenter. For such problems, it may necessary to include post-Newtonian "cross terms" in the equations of motion in order to capture relativistic effects consistently over the long timescales. Cross terms are post-Newtonian (PN) terms that explicitly couple the two-body relativistic perturbations with the Newtonian perturbations due to other bodies in the system. In this paper, we show that the total energy and the normal component of total angular momentum of a hierarchical triple system is manifestly conserved to Newtonian order over the relativistic pericenter precession timescale of the inner binary if and only if PN cross-term effects in the equations of motion are taken carefully into account.