Stationary Spinning Strings and Symmetries of Classical Spacetimes

TL;DR

This paper investigates the symmetries of stationary spacetimes using spinning string dynamics, showing how these relate to spinning point particles in effective spaces, with specific analysis of Kerr-Newman spacetime.

Contribution

It demonstrates the reduction of spinning string dynamics to spinning point particles in effective spaces and analyzes their symmetries, including Killing tensors and vectors, in the context of Kerr-Newman spacetime.

Findings

Effective space is a conformally scaled quotient of the original spacetime.

Killing tensor and spin-valued Killing vector are identified in the effective space.

Nongeneric supersymmetry from the Killing-Yano tensor is absent in the effective space.

Abstract

We explore the symmetries of classical stationary spacetimes in terms of the dynamics of a spinning string described by a worldsheet supersymmetric action. We show that for stationary configurations of the string, the action reduces to that for a pseudo-classical spinning point particle in an effective space, which is a conformally scaled quotient space of the original spacetime. As an example, we consider the stationary spinning string in the Kerr-Newman spacetime, whose motion is equivalent to that of the spinning point particle in the three-dimensional effective space. We present the Killing tensor as well as the spin-valued Killing vector of this space. However, the nongeneric supersymmetry corresponding to the Killing-Yano tensor of the Kerr-Newman spacetime is lost in the effective space.