Classical formulation of Cosmic Censorship Hypothesis

TL;DR

This paper explores the nature of spatially homothetic spacetimes, demonstrating their role in the Cosmic Censorship Hypothesis by linking gravity's scale invariance to the avoidance of naked singularities.

Contribution

It establishes the equivalence between the Cosmic Censorship Hypothesis and the principle that gravity lacks a length-scale for matter inhomogeneities, using examples of such spacetimes.

Findings

Spatially homothetic spacetimes do not form naked singularities with regular initial data.

The Cosmic Censorship Hypothesis is equivalent to gravity having no length-scale for matter properties.

Abstract

Spacetimes admitting appropriate spatial homothetic Killing vectors are called spatially homothetic spacetimes. Such spacetimes conform to the fact that gravity has no length-scale for matter inhomogeneities. The matter density for such spacetimes is (spatially) arbitrary and the matter generating the spacetime admits {\it any} equation of state. Spatially homothetic spacetimes necessarily possess energy-momentum fluxes. We first discuss spherically symmetric and axially symmetric examples of such spacetimes that do not form naked singularities for regular initial data. We then show that the Cosmic Censorship Hypothesis is {\em equivalent} to the statement that gravity has no length-scale for matter properties.