Propagation of perturbations along strings

TL;DR

This paper develops a covariant formalism to analyze how physical perturbations propagate along strings in various curved spacetimes, providing a unified wave-equation framework applicable to multiple gravitational backgrounds.

Contribution

It introduces a novel covariant approach for studying string perturbations in arbitrary curved spacetimes, including explicit wave-equation descriptions in specific backgrounds.

Findings

Perturbations follow a wave-equation with a potential comprising time-dilation and curvature terms.

The formalism is applied to Rindler, de Sitter, Schwarzschild, and Reissner-Nordstrom spacetimes.

Propagation characteristics depend on spacetime curvature and string stationarity.

Abstract

A covariant formalism for physical perturbations propagating along a string in an arbitrary curved spacetime is developed. In the case of a stationary string in a static background the propagation of the perturbations is described by a wave-equation with a potential consisting of 2 terms: The first term describing the time-dilation and the second is connected with the curvature of space. As applications of the developed approach the propagation of perturbations along a stationary string in Rindler, de Sitter, Schwarzschild and Reissner-Nordstrom spacetimes are investigated.