How Does Naked Singularity Look?

TL;DR

This paper investigates the appearance and properties of naked singularities in self-similar dust collapse, analyzing null geodesics, angular size, and frequency effects to understand their observational features.

Contribution

It provides a detailed analysis of null geodesics and the observable characteristics of naked singularities assuming self-similarity in dust collapse models.

Findings

Angular diameter bounded by Schwarzschild circular null geodesic

Frequency of propagating fields depends on impact parameter

Naked singularity topology may be non-uniform

Abstract

There are non-radial null geodesics emanating from the shell focusing singularity formed at the symmetric center in a spherically symmetric dust collapse. In this article, assuming the self-similarity in the region filled with the dust fluid, we study these singular null geodesics in detail. We see the time evolution of the angular diameter of the central naked singularity and show that it might be bounded above by the value corresponding to the circular null geodesic in the Schwarzschild spacetime. We also investigate the angular frequency of a physical field which propagates along the singular null geodesic and find that it depends on the impact parameter. Further, we comment on the non-uniformity of the topology of the central naked singularity.