Note on strong cosmic censorship for spherically symmetric Einstein-dust model

TL;DR

This paper derives differential equations for light rays in spherically symmetric dust models, demonstrating generic violations of strong cosmic censorship in these scenarios with and without a positive cosmological constant.

Contribution

It provides a new differential equation approach to analyze cosmic censorship violations in Einstein-dust models, extending previous results to include positive cosmological constant cases.

Findings

Violations of strong cosmic censorship are generic in these models.

Derived differential equations characterize light ray behavior in dust spacetimes.

Confirmed previous results and extended them to new cosmological settings.

Abstract

In this note, we derive an ordinary differential equation for outgoing light rays in the spacetime of a spherically symmetric contracting dust cloud. The violation of strong cosmic censorship is equivalent to the existence of a solution blowing up at the centre of the symmetry. As an application, we reprove the generic violation of strong cosmic censorship for a dust cloud first proved by Christodoulou. We also derive a similar equation for a spherically symmetric dust cloud in the case of positive cosmological constant and show the generic violation of strong cosmic censorship in this case.