Analytical results for string propagation near a Kaluza-Klein black hole

TL;DR

This paper derives analytical solutions for null string motion near a magnetically charged Kaluza-Klein black hole, including approximate and exact solutions, enhancing understanding of string behavior in such complex spacetimes.

Contribution

It provides the first analytical solutions for null strings in a Kaluza-Klein black hole background, including a large distance approximation and exact solutions for specific monopole cases.

Findings

Zeroth order solutions expressed in elementary functions

Exact solutions for Pollard-Gross-Perry-Sorkin monopole case

Analytical insights into string dynamics near Kaluza-Klein black holes

Abstract

This brief report presents analytical solutions to the equations of motion of a null string. The background spacetime is a magnetically charged Kaluza-Klein black hole. The string coordinates are expanded with the world-sheet velocity of light as an expansion parameter. It is shown that the zeroth order solutions can be expressed in terms of elementary functions in an appropriate large distance approximation. In addition, a class of exact solutions corresponding to the Pollard-Gross-Perry-Sorkin monopole case is also obtained.