Topological Censorship

TL;DR

This paper discusses a topological censorship principle in general relativity, showing that under certain conditions, observable topological structures are hidden from distant observers, despite being allowed by Einstein's equations.

Contribution

It proves a topological censorship theorem, demonstrating that physically reasonable isolated systems cannot have observable nontrivial topology at medium scales.

Findings

Topological structures are hidden from distant observers.

Einstein equations and energy conditions imply topological censorship.

Physically reasonable systems exhibit topological censorship.

Abstract

Classically, all topologies are allowed as solutions to the Einstein equations. However, one does not observe any topological structures on medium range distance scales, that is scales that are smaller than the size of the observed universe but larger than the microscopic scales for which quantum gravity becomes important. Recently, Friedman, Schleich and Witt have proven that there is topological censorship on these medium range distance scales: the Einstein equations, locally positive energy, and local predictability of physics imply that any medium distance scale topological structures cannot be seen. More precisely, we show that the topology of physically reasonable isolated systems is shrouded from distant observers, or in other words there is a topological censorship principle.