World-line perturbation theory

TL;DR

This paper develops a perturbation theory for the world lines of compact bodies in curved spacetime, addressing the challenges of modeling finite-sized objects in General Relativity.

Contribution

It introduces a perturbative approach based on generalized geodesic deviation equations for constructing world lines of extended bodies.

Findings

Applicable to test masses and spinning bodies

Provides a framework for approximate solutions in curved spacetimes

Addresses limitations of point-particle models in General Relativity

Abstract

The motion of a compact body in space and time is commonly described by the world line of a point representing the instantaneous position of the body. In General Relativity such a world-line formalism is not quite straightforward because of the strict impossibility to accommodate point masses and rigid bodies. In many situations of practical interest it can still be made to work using an effective hamiltonian or energy-momentum tensor for a finite number of collective degrees of freedom of the compact object. Even so exact solutions of the equations of motion are often not available. In such cases families of world lines of compact bodies in curved space-times can be constructed by a perturbative procedure based on generalized geodesic deviation equations. Examples for simple test masses and for spinning test bodies are presented.