The form of cosmic string cusps

TL;DR

This paper classifies cosmic string cusp shapes, analyzes their Lorentz transformations, and recalculates the energy release during cusp events, finding that radiation is suppressed due to Lorentz contraction effects.

Contribution

It provides a comprehensive classification of cosmic string cusp geometries and a revised calculation of energy release, highlighting the suppression of observable radiation.

Findings

Cusp shapes can be classified with a generic form where motion lies in the cusp plane.

Energy released near cusps scales as  r^{1/2}L^{1/2}, not r^{1/3}L^{2/3}.

Radiation from cusps is strongly suppressed for cosmological strings.

Abstract

We classify the possible shapes of cosmic string cusps and how they transform under Lorentz boosts. A generic cusp can be brought into a form in which the motion of the cusp tip lies in the plane of the cusp. The cusp whose motion is perpendicular to this plane, considered by some authors, is a special case and not the generic situation. We redo the calculation of the energy in the region where the string overlaps itself near a cusp, which is the maximum energy that can be released in radiation. We take into account the motion of a generic cusp and the resulting Lorentz contraction of the string core. The result is that the energy scales as $\sqrt {rL}$ instead of the usual value of $r^{1/3} L^{2/3}$, where $r$ is the string radius and $L$ and is the typical length scale of the string. Since $r << L $ for cosmological strings, the radiation is strongly suppressed and could not be observed.