Observers in Kerr spacetimes: the ergoregion on the equatorial plane

Abstract

We perform a detailed analysis of the properties of stationary observers located on the equatorial plane of the ergosphere in a Kerr spacetime, including light-surfaces. This study highlights crucial differences between black hole and the super-spinner sources. In the case of Kerr naked singularities, the results allow us to distinguish between "weak" and "strong " singularities, corresponding to spin values close to or distant from the limiting case of extreme black holes, respectively. We derive important limiting angular frequencies for naked singularities. We especially study very weak singularities as resulting from the spin variation of black holes. We also explore the main properties of zero angular momentum observers for different classes of black hole and naked singularity spacetimes.

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

“…A ZAMO, well defined in the ergoregion, corotates with the BH. ZAMOs have interesting properties in the case of slowly spinning naked singularities and certainly offer a particularly appropriate and convenient description of the spacetime in the ergoregion -see for example [16,18] and [42][43][44][45][46][47][48][49][50][51][52][53][54]. Static observers are defined by the limiting condition ω = 0 and cannot exist in the ergoregion.…”

“…On the other hand, the radii r ± II : ∂ 2 ω r ± s = 0 and, analogously, ω ± II : ∂ 2 r ω ± = 0 characterize the curvatures of the curves ω ± and r ± s . Killing bottlenecks, identified in [18] as ripples in the r−ω plane (see Figs. 3 and 4), were interpreted in the BL frame as "remnants" of the disconnection between the Killing throat present in BH-geometries and the singular bottleneck of the extreme BH.…”

Constraining LQG Graph with Light Surfaces: Properties of BH Thermodynamics for Mini-Super-Space, Semi-Classical Polymeric BH

“…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].…”