2014/07/31 by Emmanuele Battista, Giampiero Esposito
Mathematics · Physics and Astronomy · #Applied mathematics #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Equations of motion #Field (mathematics) #Gravitational field #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Motion (physics) #Newtonian fluid #Physics #Pulsars and Gravitational Waves Research #Pure mathematics #Quantum mechanics #Two-body problem #Work (physics) #gr-qc #hep-th #n-body problem
paper · pdf · doi:10.1103/physrevd.90.084010
published as Phys.Rev. D90 (2014) 084010 · 23 pages, 1 figure, Revtex4. In the final version, Section VII is much longer, the misprints have been amended, and new References have been included
arxiv created 2014/09/25 · openalex publication_date 2014/10/09 · arxiv updated 2014/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Recent work in the literature has studied the restricted three-body problem within the framework of effective-field-theory models of gravity. This paper extends such a program by considering the full three-body problem, when the Newtonian potential is replaced by a more general central potential which depends on the mutual separations of the three bodies. The general form of the equations of motion is written down, and they are studied when the interaction potential reduces to the quantum-corrected central potential considered recently in the literature. A recursive algorithm is found for solving the associated variational equations, which describe small departures from given periodic solutions of the equations of motion. Our scheme involves repeated application of a 2\ifmmode×\else\texttimes\fi2 matrix of first-order linear differential operators.