TRACING TOWARDS THE SHADOW EDGE OF KERR BLACK HOLES AND NAKED SINGULARITIES

Abstract

Direct imaging of supermassive black holes (SMBHs) at event horizon-scale resolutions, as recently done by the Event Horizon Telescope, allows for constraining SMBH parameters like spin and observational inclination angles, as well as alternative models to SMBHs such as Kerr naked singularities (KNSs). KNSs are theoretical objects which arise when Kerr (spinning) black holes spins so fast that its event horizon vanishes due to the extreme frame dragging effects, leaving behind naked singularities. In this thesis, we review null geodesics in Kerr spacetime and their connections to the projection of the unstable spherical photon orbits to an image plane at infinity, which we define to be the “shadow”. We then extend previous analysis of Kerr shadows to KNSs, demonstrating 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 ≲ 1.18 and vanishing for a ≳ 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 for the very first time. The critical spin that distinguishes closed and open shadows turns out to be the same spin a = √6√3 − 9 ≈ 1.18 where polar photon orbits disappear as computed by Charbulak & Stuchlik (2018). 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. We conclude with a brief discussion on the future prospects in imaging higher-order photon rings with space-based radio arrays and their implications for constraining possible deviation from the Kerr metric. This thesis is based on “Shadow Geometry of Kerr Naked Singularities”, which was published on the Astrophysical Journal, Volume 954, Issue 1, id. 78 (Nguyen et al. 2023).