Hidden Symmetry and Exact Solutions in Einstein Gravity

TL;DR

This paper explores hidden symmetries in higher-dimensional rotating black holes using conformal Killing-Yano tensors, providing a classification and exact solutions to Einstein's equations that reveal new geometric structures.

Contribution

It introduces conformal Killing-Yano tensors as a framework for understanding symmetries in higher-dimensional black hole spacetimes and presents new exact solutions.

Findings

Classification of spacetimes with conformal Killing-Yano tensors

Derivation of exact Einstein solutions for these spacetimes

Identification of hidden symmetries in higher dimensions

Abstract

Conformal Killing-Yano tensors are introduced as a generalization of Killing vectors. They describe symmetries of higher-dimensional rotating black holes. In particular, a rank-2 closed conformal Killing-Yano tensor generates the tower of both hidden symmetries and isometries. We review a classification of higher-dimensional spacetimes admitting such a tensor, and present exact solutions to the Einstein equations for these spacetimes.