Transonic Elastic Model for Wiggly Goto-Nambu String

TL;DR

This paper establishes a solid mathematical foundation for modeling wiggly Goto-Nambu cosmic strings as transonic elastic strings, clarifying a previously debated proposition.

Contribution

It provides a rigorous mathematical validation for representing wiggly Goto-Nambu strings with transonic elastic string models.

Findings

Mathematical proof of the transonic elastic string model validity

Clarification of the energy density and tension relationship

Resolution of previous controversies in string modeling

Abstract

The hitherto controversial proposition that a ``wiggly" Goto-Nambu cosmic string can be effectively represented by an elastic string model of exactly transonic type (with energy density $U$ inversely proportional to its tension $T$) is shown to have a firm mathematical basis.