Cosmic Censorship in 2-Dimensional Dilaton Gravity

TL;DR

This paper investigates the structure of 2D dilaton gravity, demonstrating a local cosmic censorship principle where positive energy leads to trapped spatial singularities cloaked by horizons, akin to black hole formation.

Contribution

It introduces a positive-definite gravitational energy, defines trapped points, and shows how matter collapse results in cloaked spatial singularities in 2D dilaton gravity.

Findings

Spatial singularities are trapped and cloaked by horizons.

Gravitational energy is positive at spatial singularities.

Matter collapse creates cloaked spatial singularities with non-decreasing area.

Abstract

The global structure of 2-dimensional dilaton gravity is studied, attending in particular to black holes and singularities. A gravitational energy is defined and shown to be positive at spatial singularities and negative at temporal singularities. Trapped points are defined, and it is shown that spatial singularities are trapped and temporal singularities are not. Thus a local form of cosmic censorship holds for positive energy. In an analogue of gravitational collapse to a black hole, matter falling into an initially flat space creates a spatial curvature singularity which is cloaked in a spatial or null apparent horizon with non-decreasing energy and area.