Naked and truly naked rotating black holes

TL;DR

This paper explores the properties of rotating black holes with naked horizons, analyzing how curvature components and algebraic types behave near the horizon from different observer perspectives using the Newman-Penrose formalism.

Contribution

It generalizes previous static black hole results to include rotation and examines the behavior of curvature and algebraic type near horizons for various observers.

Findings

Curvature components can diverge for falling observers near rotating black hole horizons.

The algebraic type of the spacetime can change due to local Lorentz boosts near the horizon.

Analysis of Weyl scalars reveals observer-dependent singular behaviors.

Abstract

Previously, it was noticed that in some space-times with Killing horizons some curvature components, responsible for tidal forces, small or even zero in the static frame, become enhanced from the viewpoint of a falling observer. This leads to the notion of so-called naked black holes. If some components in the frame attached to a free-falling observer formally diverge, although scalar invariants remain finite, such space-times was named "truly naked black holes" (in mathematical language, one can speak about non-scalar singularity). Previous results included static spherically symmetric or distorted static metrics. In the present work, we generalized them to include rotation in consideration. We also scrutiny how the algebraic type can change in the vicinity of the horizon due to local Lorentz boost. Our approach essentially uses the Newman-Penrose formalism, so we analyze the behavior of Weyl scalar for different kinds of observers.