Ricci-Weyl curvature balance in viscous dissipative collapse: A covariant analysis of singularity censorship

TL;DR

This work investigates cosmic censorship in spherically symmetric collapse with shear and bulk viscosity and heat flux using the 1+1+2 semi-tetrad covariant formalism. It derives a master equation for the Weyl scalar and reveals a curvature balance between Ricci (matter) and Weyl (free gravity) components on the apparent horizon, captured by the criterion $R+6E$ as a local indicator of nakedness. The analysis connects MOTS evolution to matter content through ratios like $ frac{\alpha}{\beta}$ and establishes necessary and sufficient covariant conditions for a central singularity to be locally naked, finding a weaker form of cosmic censorship in dissipative collapse. The results show viscosity actively modulates horizon formation by coupling to curvature, with implications for numerical simulations and potential links to quantum gravity near extremes where Weyl curvature dominates.

Abstract

We investigate the cosmic censorship conjecture in a spherically symmetric collapse with shear and bulk viscosity, heat flux, and pressure anisotropy, imposing physically reasonable energy conditions. Using the semi-tetrad covariant formalism, we derive the dynamics of the collapsing fluid, including a master equation for the evolution of the Weyl curvature, to examine the role of viscosity. The analysis of null geodesic geometry uncovers a novel curvature-balance mechanism between Ricci (matter) and Weyl (free gravitational field) curvature on the apparent horizon; this balance determines the causal nature of the horizon and thereby governs the visibility of the singularity. We then derive necessary and sufficient covariant conditions for the central singularity to be locally naked. Our findings support a weaker form of cosmic censorship and extend the covariant censorship analysis to realistic dissipative, viscous collapse.