Dynamics of Toroidal Spiral Strings around Five-dimensional Black Holes

TL;DR

This paper investigates the mathematical separability and dynamics of toroidal spiral strings, especially Hopf loop strings, around five-dimensional black holes, revealing conditions for complete variable separation and providing explicit solutions.

Contribution

It demonstrates the complete separation of variables for Hopf loop strings in specific five-dimensional black hole backgrounds and derives explicit solutions for their dynamics.

Findings

Complete variable separation for Hopf loop strings in Kerr and Kerr-AdS backgrounds with equal angular momenta.

Explicit dynamical solutions for Hopf loop strings around black holes.

Analysis of string behavior in Minkowski spacetime for general toroidal spirals.

Abstract

We examine the separability of the Nambu-Goto equation for test strings in a shape of toroidal spiral in a five-dimensional Kerr-AdS black hole. In particular, for a `{\it Hopf loop}\rq string which is a special class of the toroidal spiral strings, we show the complete separation of variables occurs in two cases, Kerr background and Kerr-AdS background with equal angular momenta. We also obtain the dynamical solution for the Hopf loop around a black hole and for the general toroidal spiral in Minkowski background.