Notes on Cosmic Censorship Conjecture revisited: Covariantly

TL;DR

This paper investigates the dynamics of trapped regions in LRS class II spacetimes, emphasizing the role of Weyl curvature in the visibility of singularities during gravitational collapse.

Contribution

It introduces a covariant, frame-independent formalism to analyze apparent horizons and establishes conditions for local nakedness of singularities, highlighting Weyl curvature's significance.

Findings

Weyl curvature influences the deformation and delay of trapped regions.

Conditions for a singularity to be locally naked are quantitatively established.

Covariant geometrical results for apparent horizons are proven.

Abstract

In this paper we study the dynamics of the trapped region using a frame independent semi-tetrad covariant formalism for general Locally Rotationally Symmetric (LRS) class II spacetimes. We covariantly prove some important geometrical results for the apparent horizon, and state the necessary and sufficient conditions for a singularity to be locally naked. These conditions bring out, for the first time in a quantitative and transparent manner, the importance of the Weyl curvature in deforming and delaying the trapped region during continual gravitational collapse, making the central singularity locally visible.