Naked and truly naked rotating black holes

TL;DR

This work extends the naked and truly naked horizon concepts from static to rotating axially symmetric spacetimes by employing the Newman–Penrose formalism and frame transformations to a free-falling observer. It derives explicit near-horizon expansions and finiteness conditions for the Riemann tensor, encoded in Weyl and Ricci scalars, and provides a four-scalar classification of horizons based on boosted NP quantities. The study maps out how off-horizon and on-horizon algebraic (Petrov) types can differ under local boosts and establishes consistency with known static results. The framework clarifies when tidal forces diverge, remain finite, or vanish at the horizon, highlighting nonscalar (non-invariant) aspects of horizon regularity with potential implications for strong gravity and quantum gravity considerations.

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.