Toroidal Spiral Strings in Higher-dimensional Spacetime

TL;DR

This paper investigates the separability of the Nambu-Goto equation for toroidal spiral strings in five-dimensional Kerr-AdS black holes, providing solutions and conditions for complete variable separation.

Contribution

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

Findings

Complete separation of variables in Kerr and Kerr-AdS backgrounds with equal angular momenta.

Explicit dynamical solutions for Hopf loop strings around black holes.

Identification of conditions for separability of toroidal spiral strings.

Abstract

We report on our progress in research of separability of the Nambu-Goto equation for test strings with a symmetric configuration in a shape of toroidal spiral in a five-dimensional Kerr-AdS black hole. In particular, for a Hopf loop string which is a special class of the toroidal spirals, 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.