String propagation near Kaluza-Klein black holes: an analytical and numerical study

TL;DR

This paper analyzes string propagation near Kaluza-Klein black holes using both analytical and numerical methods, revealing how the string's behavior varies with electric and magnetic charges and providing new solutions and insights into string dynamics in these backgrounds.

Contribution

It offers the first detailed analytical and numerical study of string motion near Kaluza-Klein black holes, including solutions for magnetic cases and perturbation analysis.

Findings

Analytical solutions for magnetic black holes using elliptical integrals.

String deceleration observed in magnetic backgrounds.

First-order perturbations affect the invariant string length.

Abstract

This paper presents a detailed investigation of the motion of a string near a Kaluza-Klein black hole, using the null string expansion. The zeroth-order string equations of motion are set up separately for electrically and magnetically charged black hole backgrounds. The case of a string falling head-on into the black hole is considered in detail. The equations reduce to quadratures for a magnetically charged hole, while they are amenable to numerical solution for an electrically charged black hole. The Kaluza-Klein radius seen by the string as it approaches the black hole decreases in the magnetic case and increases in the electric case. For magnetic backgrounds, analytical solutions can be obtained in terms of elliptical integrals. These reduce to elementary functions in special cases, including that of the well-known Pollard-Gross-Perry-Sorkin monopole. Here the string exhibits decelerated descent into the black hole. The results in the authors' earlier papers are substantiated here by presenting a detailed analysis. A preliminary analysis of first-order perturbations is also presented, and it is shown that the invariant string length receives a nonzero contribution in the first order.