Weyl Curvature and Cosmic Censorship Conjecture: A Geometrical Perspective

In search of the possible physical and geometrical factors that are responsible for the local violation of Cosmic Censorship Conjecture, this chapter delves into the gravitational collapse problem of a spherical self gravitating system via a geometrical formalism. By identifying the timelike and the preferred spacelike directions which spherically symmetric spacetime manifolds covariantly possess, we perform a local semi-tetrad decomposition of the spacetime. Through the geometrical quantities associated with these vector fields and the thermodynamic quantities of the collapsing matter, we analyse the null geodesics in the collapsing spacetime and the geometry of the marginally outer trapped surface. We transparently and quantitatively identify the role of Weyl curvature in deforming this surface in such a way that the central singularity can be locally naked. Further to this, we relate the local violation of censorship with thermodynamics of gravity by assuming that the energy momentum tensor of the free gravitational field is given by the square root of the Bel-Robinson tensor. This provides a novel thermodynamic picture of the local violation of censorship, which happens due to extreme domination of the free gravitational energy over the matter energy.