Disclosing connections between black holes and naked singularities: horizon remnants, Killing throats and bottlenecks

Abstract

We study the properties of black holes and naked singularities by considering stationary observers and light surfaces in Kerr spacetimes. We reconsider the notion of Killing horizons from a special perspective by exploring the entire family of Kerr metrics. To this end, we introduce the concepts of extended plane, Killing throats and bottlenecks for weak (slowly spinning) naked singularities. Killing bottlenecks (or horizon remnants in analogy with the corresponding definition of throats in black holes) are restrictions of the Killing throats appearing in special classes of slowly spinning naked singularities. Killing bottlenecks appear in association with the concept of pre-horizon regime introduced in [1, 2]. In the extended plane of the Kerr spacetime, we introduce particular sets, metric bundles, of metric tensors which allow us to reinterpret the concept of horizon and to find connections between black holes and naked singularities throughout the horizons. To evaluate the effects of frame-dragging on the formation and structure of Killing bottlenecks and horizons in the extended plane, we consider also the Kerr-Newman and the Reissner-Norström spacetimes. We argue that these results might be significant for the comprehension of processes that lead to the formation and eventually destruction of Killing horizons. * Electronic address: d.pugliese.

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“…The orbital frequency can be measured related to the local causal structure by an observer locally, and in a point of the extended plane which is a plane P − r, where the MBs are defined as curves, P is the metrics family parameter, and r is a radial distance. In this application, as in [6][7][8][9][10][11], the bundles are defined as the sets of all geometries having equal limiting light-like orbital frequency, which is also an asymptotic limiting value for time-like stationary observers (as measured at infinity). MBs are conformal invariant and can be easily read in terms of the light surfaces (LS), related to the analysis of many aspects of BHs physics, as "BH" images and several processes constraining energy extraction as the BH jet emission and jet collimation.…”

“…MBs are conformal invariant and can be easily read in terms of the light surfaces (LS), related to the analysis of many aspects of BHs physics, as "BH" images and several processes constraining energy extraction as the BH jet emission and jet collimation. The role of MBs is clear in the geometries with Killing horizons as the Kerr geometries, and more generally in the axially symmetric spacetimes as the Kerr-Newman (KN) geometry and Kerr-de-Sitter geometry [6][7][8][9][10][11]. The MBs definition to the spherical symmetric cases considered here for the regular BH is not immediate.…”

“…Spherically symmetric BHs solutions have generally a direct astrophysical interest as limiting conditions for the spinning BHs. In [6][7][8]11], the Schwarzschild geometry in MBs analysis has been considered as limiting solution for the axially symmetric Kerr geometry or the Kerr-Newman geometry, or also the Reissner-Nordström family. Schwarzschild geometry is represented as a point on the horizon in the extended plane for all these solutions [12,13].…”

“…Below we discuss more precisely some main notions on metric bundles. Introduced in [6] to explain some properties of black holes and naked singularities (NSs), MBs establish a relation between these. Their definition was first based on the investigation of the limiting frequencies of stationary observers, and define the Killing horizons for the Kerr black holes and then extended the to other exact solutions as the cosmological Kerr-de-Sitter, the Kerr Newman spacetimes, and the limiting case of Reissner-Norström solutions [6][7][8][9][10][11].…”