Conformal diagrams for the gravitational collapse of a spherically symmetric dust cloud

TL;DR

This paper introduces an algorithm to construct conformal diagrams for spherically symmetric dust cloud collapse in general relativity, enabling analysis of the causal structure of such spacetimes.

Contribution

The paper presents a novel numerical algorithm for generating conformal diagrams of collapsing dust clouds, facilitating causal analysis in gravitational collapse scenarios.

Findings

Conformal diagrams reveal the causal structure of collapsing dust clouds.

The algorithm accurately models null geodesics in collapsing spacetimes.

Analysis of diagrams provides insights into black hole formation and horizon development.

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 radial null geodesics. As an application we generate conformal diagrams for collapsing spherical dust clouds and analyze the causal structure of the resulting spacetimes.