Can a self-gravitating thin cosmic string obey the Nambu-Goto dynamics ?

TL;DR

This paper investigates the conditions under which a self-gravitating thin cosmic string follows Nambu-Goto dynamics, showing that specific constraints lead to Nambu-Goto behavior, while unconstrained models result in totally geodesic world sheets.

Contribution

It demonstrates that imposing a particular constraint on a self-gravitating string model results in Nambu-Goto dynamics in the thin limit, clarifying the conditions for such behavior.

Findings

Constrained models obey Nambu-Goto dynamics as radius tends to zero.

Unconstrained models have totally geodesic world sheets.

The thin limit behavior depends on the imposed constraints.

Abstract

We assume that a self-gravitating string is locally described by a thin tube of matter represented by a ``smoothed conical metric''. If we impose a specific constraint on the model of string then its central line obeys the Nambu-Goto dynamics in the limit where the radius of the tube tends to zero. If no constraint is added then the world sheet of the central line is totally geodesic.