Probabilistic view on singularities and spacetime boundary

TL;DR

This paper introduces probabilistic methods to study singularities and spacetime boundaries in general relativity, proving new theorems and defining a boundary concept free of classical defects.

Contribution

It presents two novel singularity theorems using probabilistic techniques and introduces a new probabilistic spacetime boundary concept.

Findings

Probabilistic methods can establish singularity theorems without causal assumptions.

Simple energy flow conditions imply probabilistic incompleteness.

A new probabilistic spacetime boundary avoids classical pathologies.

Abstract

The aim of this article is to promote the use of probabilistic methods in the study of problems in mathematical general relativity. Two new and simple singularity theorems, whose features are different from the classical singularity theorems, are proved using probabilistic methods. Under some energy conditions, and without any causal or initial/boundary assumption, simple conditions on the energy flow imply probabilistic incompleteness. Also we introduce a probabilistic notion of spacetime boundary which has none of the pathological defects that the classical boundaries may have.