The motion of relativistic strings in curved space-times

TL;DR

This paper studies the equations governing relativistic strings in curved space-times, proving global existence of smooth solutions and analyzing specific cases like Ori's space-time.

Contribution

It provides a general framework for relativistic string equations in Lorentzian manifolds and establishes conditions for global smooth solutions, including in Ori's space-time.

Findings

Proved global existence of smooth solutions in curved space-times.

Analyzed properties of relativistic string equations.

Derived conditions for solutions in Ori's space-time.

Abstract

This paper concerns the motion of a relativistic string in a curved space-time. As a general framework, we first analyze relativistic string equations, i.e., the basic equations for the motion of a one-dimensional extended object in a curved enveloping space-time $(\mathscr{N}, \tilde g)$, which is a general Lorentzian manifold, and then investigate some interesting properties enjoyed by these equations. Based on this, under suitable assumptions we prove the global existence of smooth solutions of the Cauchy problem for relativistic string equations in the curved space-time $(\mathscr{N}, \tilde g)$. In particular, we consider the motion of a relativistic string in the Ori's space-time, and give a sufficient and necessary condition guaranteeing the global existence of smooth solutions of the Cauchy problem for relativistic string equations in the Ori's space-time.