Higher-dimensional black holes with multiple equal rotations

TL;DR

This paper investigates a special limit of higher-dimensional Kerr-(A)dS black holes with multiple equal rotations, revealing a complex structure with preserved symmetries and evidence of enhanced symmetry in six dimensions.

Contribution

It introduces a new class of solutions with equal rotations, preserving the full symmetry structure and uncovering potential symmetry enhancement in six dimensions.

Findings

The metric splits into two parts with different geometric interpretations.

The full set of symmetries, including Killing vectors and tensors, is preserved.

In six dimensions, additional symmetries and reducibility of Killing tensors are observed.

Abstract

We study a limit of the Kerr-(A)dS spacetime in a general dimension where an arbitrary number of its rotational parameters is set equal. The resulting metric after the limit formally splits into two parts - the first part has the form of the Kerr-NUT-(A)dS metric analogous to the metric of the entire spacetime, but only for the directions not subject to the limit, and the second part can be interpreted as the K\"{a}hler metrics. However, this separation is not integrable, thus it does not lead to a product of independent manifolds. We also reconstruct the original number of explicit and hidden symmetries associated with Killing vectors and Killing tensors. Therefore, the resulting spacetime represents a special subcase of the generalized Kerr-NUT-(A)dS metric that retains the full Killing tower of symmetries. In $D=6$, we present evidence of an enhanced symmetry structure after the limit. Namely, we find additional Killing vectors and show that one of the Killing tensors becomes reducible as it can be decomposed into Killing vectors.