Kerr metric bundles. Killing horizons confinement, light-surfaces and horizons replicas

TL;DR

This paper characterizes Kerr metric bundles, revealing how horizons and frequencies relate, and explores their potential for detecting inner horizons and understanding black hole thermodynamics.

Contribution

It introduces the concept of metric bundles in Kerr spacetimes, linking horizon frequencies to spacetime geometry and proposing methods to detect inner horizon features.

Findings

Horizon frequencies define metric bundles and their envelopes.

Inner horizon confinement and horizon replicas can be detected via emission spectra.

Detection is feasible near the rotation axis depending on black hole spin.

Abstract

We provide a complete characterization of the metric Killing bundles (or metric bundles) of the Kerr geometry. Metric bundles, first introduced in [21] 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. 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.