# Spinning and Spinning Deviation Equations of Bi-metric Type Theories

## TL;DR

This paper derives spinning and deviation equations for bi-metric gravity theories, examining how different curvature and affine connections influence spinning motions, and proposes specific Lagrangians for these theories.

## Contribution

It introduces new spinning and deviation equations for bi-metric gravity theories and analyzes the effects of various curvatures and affine connections.

## Key findings

- Derived spinning equations analogous to Papapetrou equations
- Analyzed influence of different curvatures and affine connections
- Proposed specific Lagrangian functions for each bi-metric theory

## Abstract

Spinning equations of bi-metric types theories of gravity, the counterpart of the Papapetrou spinning equations of motion have been derived as well as their corresponding spinning deviation equations. Due to introducing different types of bi-metric theories, the influence of different curvatures based upon different affine connections , have been examined. A specific Lagrangian function for each type theory has been proposed, in order to derive the set of spinning motions and their corresponding spinning deviation equations.