Stationary strings and branes in the higher-dimensional Kerr-NUT-(A)dS spacetimes

TL;DR

This paper proves the complete integrability of stationary strings and certain p-branes in higher-dimensional Kerr-NUT-(A)dS black hole spacetimes, revealing hidden symmetries and reducing the problem to geodesic equations.

Contribution

It demonstrates the integrability of stationary strings and introduces the concept of $\xi$-branes in higher-dimensional Kerr-NUT-(A)dS spacetimes, linking symmetries to geodesic problems.

Findings

Stationary string equations are integrable in Kerr-NUT-(A)dS backgrounds.

Hidden symmetries inherited from black hole spacetimes enable this integrability.

The concept of $\xi$-branes extends the analysis to p-branes with mutually commuting Killing vectors.

Abstract

We demonstrate complete integrability of the Nambu-Goto equations for a stationary string in the general Kerr-NUT-(A)dS spacetime describing the higher-dimensional rotating black hole. The stationary string in D dimensions is generated by a 1-parameter family of Killing trajectories and the problem of finding a string configuration reduces to a problem of finding a geodesic line in an effective (D-1)-dimensional space. Resulting integrability of this geodesic problem is connected with the existence of hidden symmetries which are inherited from the black hole background. In a spacetime with p mutually commuting Killing vectors it is possible to introduce a concept of a $\xi$-brane, that is a p-brane with the worldvolume generated by these fields and a 1-dimensional curve. We discuss integrability of such $\xi$-branes in the Kerr-NUT-(A)dS spacetime.