Numerical Prediction of cusps or kinks in the Nambu-Goto dynamics

TL;DR

This paper introduces a model based on the generalized Raychaudhuri equation to predict the formation of cusps and kinks in Nambu-Goto string dynamics, incorporating higher order curvature effects and validating with three examples.

Contribution

It extends the generalized Raychaudhuri equation to include higher curvature terms, providing a new tool to analyze cusp and kink formation in string evolution.

Findings

Successfully predicts cusp and kink formation in tested examples

Shows higher curvature terms influence the development of singularities

Provides a graphical validation of the proposed model

Abstract

It is known that Nambu-Goto extended objects present some pathological structures, such as cusps and kinks, during their evolution. In this paper, we propose a model through the generalized Raychaudhuri equation [Rh] for membranes to determine if there are cusps and kinks in the world-sheet. We extend the generalized Rh equation for membranes to allow the study of the effect of higher order curvature terms in the action on the issue of cusps and kinks, using it as a tool for determining when a Nambu-Goto string generates cusps or kinks in its evolution. Furthermore, we present three examples where we test graphically this approach.