Dynamics of Extended Objects in General Relativity

TL;DR

This thesis reviews the dynamics of extended objects in general relativity, focusing on multipole expansions, definitions of physical quantities, and equations of motion, without introducing new theoretical developments.

Contribution

It provides a comprehensive review of multipole methods and equations of motion for extended bodies in general relativity, consolidating existing knowledge.

Findings

Derived equations of motion for extended bodies using multipole moments

Defined relativistic concepts of momentum, angular momentum, and center of mass

Presented multipole expansions for dynamical skeletons in gravitational fields

Abstract

In this thesis, multipole expansions of mass, momentum and stress density will be made for a body in Newtonian mechanics. Using these definitions; momentum, angular momentum, center of mass, force and torque are defined for $N$ gravitationally interacting isolated bodies. Equations of motions of such a system are derived. Definitions of momentum, angular momentum, center of mass, force and torque are made in a relativistic theory. Dynamical (gravitational) skeleton is defined and the multipole moments of the dynamical skeleton are found. Equations of motion for a test body moving in a gravitational field are derived in terms of the multipole moments. Save the details of the derivations, no originality in this thesis is claimed: it is intended as a review of the subject.