Action principle formulation for motion of extended bodies in General Relativity

TL;DR

This paper develops an action principle approach to describe the motion of extended bodies in weak gravitational fields within General Relativity, deriving classical equations and quantum phase shifts for multipole moments.

Contribution

It introduces a novel action principle framework that includes higher-order multipole moments and their effects on motion and quantum interference in weak gravitational fields.

Findings

Derived equations of motion for multipole moments of arbitrary order.

Identified a new force due to the octupole moment.

Predicted gravitationally induced phase shifts in quantum interference experiments.

Abstract

We present an action principle formulation for the study of motion of an extended body in General Relativity in the limit of weak gravitational field. This gives the classical equations of motion for multipole moments of arbitrary order coupling to the gravitational field. In particular, a new force due to the octupole moment is obtained. The action also yields the gravitationally induced phase shifts in quantum interference experiments due to the coupling of all multipole moments.