Action based approach to the dynamics of extended bodies in General Relativity

TL;DR

This paper introduces an action principle for modeling the motion of extended bodies with multipole moments in weak gravitational fields, linking classical dynamics with quantum phase effects and enabling quantization.

Contribution

It presents the first action-based formulation for extended bodies with multipole moments in gravity, bridging classical and quantum descriptions.

Findings

Derivation of equations of motion from the action principle.

Prediction of quantum phase shifts due to gravitational coupling.

Framework for quantizing the dynamics of extended bodies in gravity.

Abstract

We present, for the first time, an action principle that gives the equations of motion of an extended body possessing multipole moments in an external gravitational field, in the weak field limit. From the action, the experimentally observable quantum phase shifts in the wavefunction of an extended object due to the coupling of its multipole moments with the gravitational field are obtained. Also, since the theory may be quantized using the action, the present approach is useful in the interface between general relativity and quantum mechanics.