The study of higher-dimensional black holes is a subject which has recently attracted vast interest. Perhaps one of the most surprising discoveries is a realization that the properties of higher-dimensional black holes with the spherical horizon topology and described by the Kerr–NUT–(A)dS metrics are very similar to the properties of the well known four-dimensional Kerr metric. This remarkable result stems from the existence of a single object called the principal tensor. In our review we discuss explicit and hidden symmetries of higher-dimensional Kerr–NUT–(A)dS black hole spacetimes. We start with discussion of the Killing and Killing–Yano objects representing explicit and hidden symmetries. We demonstrate that the principal tensor can be used as a “seed object” which generates all these symmetries. It determines the form of the geometry, as well as guarantees its remarkable properties, such as special algebraic type of the spacetime, complete integrability of geodesic motion, and separability of the Hamilton–Jacobi, Klein–Gordon, and Dirac equations. The review also contains a discussion of different applications of the developed formalism and its possible generalizations.

高维黑洞的研究是最近引起人们广泛兴趣的一个课题。也许最令人惊讶的发现之一是认识到具有球形视界拓扑并由 Kerr–NUT–(A)dS 度量描述的高维黑洞的属性与众所周知的四维黑洞的属性非常相似。克尔度量。这一显着的结果源于一个称为主张量的单一对象的存在。在我们的综述中，我们讨论了高维 Kerr-NUT-(A)dS 黑洞时空的显式和隐式对称性。我们首先讨论 Killing 和 Killing-Yano 对象，这些对象代表显式和隐式对称性。我们证明主张量可以用作生成所有这些对称性的“种子对象”。它决定了几何的形式，并保证了其显着的性质，例如时空的特殊代数类型、测地运动的完全可积性以及汉密尔顿-雅可比、克莱因-戈登和狄拉克方程的可分离性。该评论还包含对已发展的形式主义的不同应用及其可能的概括的讨论。