Dynamics of a self-gravitating thin cosmic string

TL;DR

This paper explores the geometric and dynamical properties of self-gravitating thin cosmic strings, showing that under certain constraints, their evolution follows Nambu-Goto equations, while without constraints, their worldsheet is totally geodesic.

Contribution

It introduces the concept of a smoothed cone to model self-gravitating strings and analyzes their behavior under different constraints, revealing conditions for Nambu-Goto dynamics.

Findings

String worldsheet can be a totally geodesic surface without constraints.

Imposing specific constraints leads to Nambu-Goto equations for the string.

The model provides a geometric interpretation of self-gravitating string dynamics.

Abstract

We assume that a self-gravitating thin string can be locally described by what we shall call a smoothed cone. If we impose a specific constraint on the model of the string, then its central line obeys the Nambu-Goto equations. If no constraint is added, then the worldsheet of the central line is a totally geodesic surface.