Shadow Geometry of Kerr Naked Singularities

TL;DR

This paper explores the unique and variable shadow geometries of Kerr naked singularities, proposing observational signatures that could distinguish them from black holes and test fundamental cosmic censorship principles.

Contribution

It introduces a detailed analysis of KNS shadow topologies, including conditions for open, closed, or vanishing shadows, and connects light geodesics with shadow features through analytical and numerical methods.

Findings

KNS shadows can be open, closed, or vanish depending on spin and inclination.

A critical spin value (~1.18) determines shadow topology changes.

Numerical ray tracing confirms analytical predictions and reveals observational features.

Abstract

Direct imaging of supermassive black holes (SMBHs) at event horizon scale resolutions, as recently done by the Event Horizon Telescope, allows for testing alternative models to SMBHs such as Kerr naked singularities (KNSs). We demonstrate that the KNS shadow can be closed, open, or vanishing, depending on the spins and observational inclination angles. We study the critical parameters where the KNS shadow opens a gap, a distinctive phenomenon that does not happen with the black hole shadow. We show that the KNS shadow can only be closed for dimensionless spin $a \lesssim 1.18$ and vanishing for $a \gtrsim 1.18$ for certain ranges of inclination angles. We further analyze the effective angular momentum of photon orbits to demonstrate the fundamental connections between light geodesics and the KNS shadow geometry. We also perform numerical general relativistic ray tracing calculations, which reproduce the analytical topological change in the KNS shadow and illustrate other observational features within the shadow due to the lack of an event horizon. By comparing with black hole shadow observations, the topological change in the shadow of KNSs can be used to test the cosmic censorship hypothesis and KNSs as alternative models to SMBHs.