Full three-body problem in effective-field-theory models of gravity

TL;DR

This paper extends the study of the three-body problem in gravity models by analyzing the full problem with quantum-corrected potentials, providing a recursive algorithm for small deviations from periodic solutions.

Contribution

It introduces a general framework for the full three-body problem with effective-field-theory potentials and develops a recursive method to analyze small deviations from periodic solutions.

Findings

Derived equations of motion with quantum-corrected potentials.

Developed a recursive algorithm for variational equations.

Analyzed small departures from periodic solutions.

Abstract

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 x 2 matrix of first-order linear differential operators.