# Generalized Papapetrou's equations of motion for an extended test body within static and isotropic metrics

## TL;DR

This paper derives generalized equations of motion for extended bodies in static, isotropic spacetimes, incorporating higher multipole moments and effective mass effects, extending classical Papapetrou equations.

## Contribution

It provides a comprehensive formulation of Papapetrou's equations for extended bodies with multipole moments in static, isotropic metrics, including effective mass considerations.

## Key findings

- Derived vector form equations for different spin conditions
- Incorporated multipole moments beyond dipole in equations
- Identified an expanded effective mass accounting for structure-field interactions

## Abstract

Applying Dixon's general equations of motion for extended bodies, we compute the Papapetrou's equations for an extended test body on static and isotropic metrics. We incorporate the force and the torque terms which involve multipole moments, beyond dipole moment, from the energy-momentum tensor. We obtain the vector form equations for both Corinaldesi-Papapetrou and Tulczyjew-Dixon spin supplementary conditions. An expanded effective mass, including interactions between the structure of the body and the gravitational field, is also found.