Space-time defects and teleparallelism

TL;DR

This paper analyzes space-time defects analogous to crystal defects within the teleparallel gravity framework, finding that their gravitational energies are zero or infinite, highlighting an analogy with material defects.

Contribution

It evaluates the gravitational energy of space-time dislocations and disclinations using TEGR, revealing their energy characteristics and analogy with material defects.

Findings

Gravitational energy of space-time dislocations is zero.

Gravitational energy of space-time disclinations is infinite.

Establishes analogy between space-time and material defects.

Abstract

We consider the class of space-time defects investigated by Puntigam and Soleng. These defects describe space-time dislocations and disclinations (cosmic strings), and are in close correspondence to the actual defects that arise in crystals and metals. It is known that in such materials dislocations and disclinations require a small and large amount of energy, respectively, to be created. The present analysis is carried out in the context of the teleparallel equivalent of general relativity (TEGR). We evaluate the gravitational energy of these space-time defects in the framework of the TEGR and find that there is an analogy between defects in space-time and in continuum material systems: the total gravitational energy of space-time dislocations and disclinations (considered as idealized defects) is zero and infinit, respectively.