Slowly rotating black holes with exact Killing tensor symmetries

TL;DR

This paper introduces a new family of slowly rotating black hole solutions that extend the Lense-Thirring spacetime, featuring exact Killing tensor symmetries and regular horizon forms, revealing how hidden symmetries emerge with rotation.

Contribution

It presents novel slowly rotating black hole metrics with exact Killing tensor symmetries, including higher-dimensional generalizations with numerous hidden symmetries.

Findings

Black hole solutions extend Lense-Thirring spacetime.

Solutions admit exact Killing tensor symmetries.

Higher dimensions have many hidden symmetries.

Abstract

We present a novel family of slowly rotating black hole solutions in four, and higher dimensions, that extend the well known Lense-Thirring spacetime and solve the field equations to linear order in rotation parameter. As "exact metrics" in their own right, the new (non-vacuum) spacetimes feature the following two remarkable properties: i) near the black hole horizon they can be cast in the, manifestly regular, Painlev\'e-Gullstrand form and ii) they admit exact Killing tensor symmetries. We show these symmetries are inherited from the principal Killing-Yano tensor of the exact rotating black hole geometry in the slow rotation limit. This provides a missing link as to how the exact hidden symmetries emerge as rotation is switched on. Remarkably, in higher dimensions the novel generalized Lense-Thirring spacetimes feature a rapidly growing number of exact irreducible rank-2, as well as higher-rank, Killing tensors -- giving a first example of a physical spacetime with more hidden than explicit symmetries.