Conformal diagrams for the gravitational collapse of a spherical dust cloud

TL;DR

This paper introduces an algorithm to construct conformal diagrams for a collapsing spherical dust cloud in general relativity, enabling detailed analysis of singularity structures and visibility conditions.

Contribution

The paper presents a novel numerical method for creating conformal diagrams in collapsing spacetimes, including a new bound on initial data for singularity visibility.

Findings

Generated conformal diagrams for dust collapse

Analyzed singularity structure in detail

Derived a new bound for initial data ensuring visibility

Abstract

We present an algorithm for the construction of conformal coordinates in the interior of a spherically symmetric, collapsing matter cloud in general relativity. This algorithm is based on the numerical integration of the radial null geodesics and a local analysis of their behavior close to the singularity. As an application, we consider a collapsing spherical dust cloud, generate the corresponding conformal diagram and analyze the structure of the resulting singularity. A new bound on the initial data which guarantees that the singularity is visible from future null infinity is also obtained.