Focusing of timelike worldsheets in a theory of strings

TL;DR

This paper explores the focusing behavior of timelike worldsheets in string theory using generalized Raychaudhuri equations, revealing conditions for such effects and drawing parallels to spacetime singularities in General Relativity.

Contribution

It introduces the concept of focusing of worldsheets in string theory and analyzes conditions for this phenomenon using generalized Raychaudhuri equations, connecting string dynamics to spacetime singularities.

Findings

Conditions for focusing of worldsheets are derived.

Explicit solutions and initial value problems are discussed.

Results resemble point particle singularity analysis in General Relativity.

Abstract

An analysis of the generalised Raychaudhuri equations for string world sheets is shown to lead to the notion of focusing of timelike worldsheets in the classical Nambu-Goto theory of strings. The conditions under which such effects can occur are obtained . Explicit solutions as well as the Cauchy initial value problem are discussed. The results closely resemble their counterparts in the theory of point particles which were obtained in the context of the analysis of spacetime singularities in General Relativity many years ago.