We provide a complete characterization of the metric Killing bundles (or metric bundles) of the Kerr geometry. Metric bundles can be generally defined for axially symmetric spacetimes with Killing horizons and, for the case of Kerr geometries, are sets of black holes (BHs) or black holes and naked singularities (NSs) geometries. Each metric of a bundle has an equal limiting photon (orbital) frequency, which defines the bundle and coincides with the frequency of a Killing horizon in the extended plane. In this plane each bundle is represented as a curve tangent to the curve that represents the horizons, which thus emerge as the envelope surfaces of the metric bundles. We show that the horizons frequency can be used to establish a connection between BHs and NSs, providing an alternative representation of such spacetimes in the extended plane and an alternative definition of the BH horizons. We introduce the concept of inner horizon confinement and horizons replicas and study the possibility of detecting their frequencies. We study the bundle characteristic frequencies constraining the inner horizon confinement in the outer region of the plane i.e. the possibility of detect frequency related to the inner horizon, and the horizons replicas, structures which may be detectable for example from the emission spectra of BHs spacetimes. With the replicas we prove the existence of photon orbits with equal orbital frequency of the horizons. It is shown that such observations can be performed close to the rotation axis of the Kerr geometry, depending on the BH spin. We argue that these results could be used to further investigate black holes and their thermodynamic properties.

我们提供了Kerr几何的公制Killing捆绑包（或公制捆绑包）的完整表征。公制束通常可以定义为具有Killing层位的轴对称时空，对于Kerr几何形状，则是黑洞（BHs）或黑洞和裸奇点（NSs）几何形状的集合。束的每个度量具有相等的限制光子（轨道）频率，该频率定义束并与扩展平面中的Killing层的频率一致。在此平面中，每个束都表示为与表示地平线的曲线相切的曲线，因此它作为公制束的包络面出现。我们表明，层位频率可用于在BH和NSs，提供扩展平面中此类时空的替代表示以及BH层级的替代定义。我们介绍了内部视界限制和视界副本的概念，并研究了检测其频率的可能性。我们研究了束特征频率，这些特征频率将内部视界限制在平面的外部区域，即检测与内部视界相关的频率的可能性，以及视界复制品，例如可以从BHs的发射光谱中检测到的结构时空。通过复制品，我们证明了存在与地平线的轨道频率相等的光子轨道。结果表明，取决于BH自旋，可以在接近Kerr几何形状的旋转轴的位置执行此类观察。我们认为这些结果可用于进一步研究黑洞及其热力学性质。