Appearance of the central singularity in spherical collapse

TL;DR

This paper investigates the structure and visibility of a naked singularity formed during inhomogeneous dust collapse, analyzing non-radial geodesics and their implications for the appearance and energy emission of the collapsing star.

Contribution

It provides an analytical and numerical study of non-radial geodesics near a naked singularity, revealing how such singularities appear and the energy they emit.

Findings

Outgoing non-radial geodesics give the singularity an appearance of an expanding ball.

The radiated energy along these geodesics decays sharply near the singularity.

Total energy escaping via non-radial null geodesics vanishes in this collapse scenario.

Abstract

We analyze here the structure of non-radial nonspacelike geodesics terminating in the past at a naked singularity formed as the end state of inhomogeneous dust collapse. The spectrum of outgoing nonspacelike null geodesics is examined analytically. The local and global visibility of the singularity is also examined by integrating numerically the null geodesics equations. The possible implications of existence of such families towards the appearance of the star in late stages of gravitational collapse are considered. It is seen that the outgoing non-radial geodesics give an appearance to the naked central singularity as that of an expanding ball whose radius reaches a maximum before the star goes within its apparent horizon. The radiated energy (along the null geodesics) is shown to decay very sharply in the neighbourhood of the singularity. Thus the total energy escaping via non-radial null geodesics from the naked central singularity vanishes in the scenario considered here.