Killing(-Yano) Tensors in String Theory

TL;DR

This paper constructs and analyzes Killing(-Yano) tensors in higher-dimensional charged black holes, revealing their properties under string dualities and their role in conserved quantities, with explicit examples for Myers-Perry black holes.

Contribution

It introduces a method to construct Killing(-Yano) tensors in higher dimensions and studies their transformation properties under string dualities, providing explicit forms for charged Myers-Perry black holes.

Findings

Killing(-Yano) tensors encode symmetries beyond isometries.

Killing tensors in higher dimensions relate to ellipsoidal coordinates.

Transformations of these tensors under string dualities are explicitly determined.

Abstract

We construct the Killing(-Yano) tensors for a large class of charged black holes in higher dimensions and study general properties of such tensors, in particular, their behavior under string dualities. Killing(-Yano) tensors encode the symmetries beyond isometries, which lead to insights into dynamics of particles and fields on a given geometry by providing a set of conserved quantities. By analyzing the eigenvalues of the Killing tensor, we provide a prescription for constructing several conserved quantities starting from a single object, and we demonstrate that Killing tensors in higher dimensions are always associated with ellipsoidal coordinates. We also determine the transformations of the Killing(-Yano) tensors under string dualities, and find the unique modification of the Killing-Yano equation consistent with these symmetries. These results are used to construct the explicit form of the Killing(-Yano) tensors for the Myers-Perry black hole in arbitrary number of dimensions and for its charged version.