Black holes, hidden symmetry and complete integrability: Brief Review

TL;DR

This review discusses how the Principal Conformal Killing-Yano tensor underpins the integrability and separability properties of higher-dimensional rotating black holes, exemplified by the Kerr-NUT-ADS metric.

Contribution

It highlights the role of the PCKYT in generating and explaining the geometric and physical properties of these black holes, connecting symmetry with integrability.

Findings

PCKYT underlies complete integrability of geodesic equations.

PCKYT enables separation of variables in field equations.

Kerr-NUT-ADS metric admits PCKYT, linking geometry and physics.

Abstract

This paper contains a brief review of the remarkable properties of higher dimensional rotating black holes with the spherical topology of the horizon. We demonstrate that these properties are connected with and generated by a special geometrical object, the Principal Conformal Killing-Yano tensor (PCKYT). The most general solution, describing such black holes, Kerr-NUT-ADS metric, admits this structure. Moreover a solution of the Einstein Equations with (or without) a cosmological constant which possesses PCKYT is the Kerr-NUT-ADS metric. This object (PCKYT) is responsible for such remarkable properties of higher dimensional rotating black holes as: (i) complete integrability of geodesic equations and (ii) complete separation of variables of the important field equations.