Stationary strings near a higher-dimensional rotating black hole

TL;DR

This paper investigates stationary string configurations around higher-dimensional rotating black holes, demonstrating the unique principal Killing string solution and analyzing angular momentum transfer that affects black hole rotation.

Contribution

It introduces a separation of variables for Nambu-Goto equations in higher-dimensional rotating black hole spacetimes and characterizes the principal Killing string as the unique regular stationary solution.

Findings

Principal Killing string is the only regular stationary string crossing the red-shift surface.

Interaction causes angular momentum transfer from black hole to string.

Black hole rotation slows down due to string interaction.

Abstract

We study stationary string configurations in a space-time of a higher-dimensional rotating black hole. We demonstrate that the Nambu-Goto equations for a stationary string in the 5D Myers-Perry metric allow a separation of variables. We present these equations in the first-order form and study their properties. We prove that the only stationary string configuration which crosses the infinite red-shift surface and remains regular there is a principal Killing string. A worldsheet of such a string is generated by a principal null geodesic and a timelike at infinity Killing vector field. We obtain principal Killing string solutions in the Myers-Perry metrics with an arbitrary number of dimensions. It is shown that due to the interaction of a string with a rotating black hole there is an angular momentum transfer from the black hole to the string. We calculate the rate of this transfer in a spacetime with an arbitrary number of dimensions. This effect slows down the rotation of the black hole. We discuss possible final stationary configurations of a rotating black hole interacting with a string.