Gravitational energy of conical defects

TL;DR

This paper uses teleparallel gravity to calculate the energy of conical defects like cosmic strings and dislocations, confirming known results for strings and finding zero energy for dislocations.

Contribution

It applies the teleparallel framework to evaluate gravitational energy of topological defects, providing new insights into their energy characteristics.

Findings

Energy per unit length of cosmic strings matches known expressions.

Dislocations in spacetime have zero total gravitational energy.

Validates teleparallel approach for topological defect energy calculations.

Abstract

The energy density of asymptotically flat gravitational fields can be calculated from a simple expression involving the trace of the torsion tensor. Integration of this energy density over the whole space yields the ADM energy. Such expression can be justified within the framework of the teleparallel equivalent of general relativity, which is an alternative geometrical formulation of Einstein's general relativity. In this paper we apply this energy density to the evaluation of the energy per unit length of a class of conical defects of topological nature, which include disclinations and dislocations (in the terminology of crystallography). Disclinations correspond to cosmic strings, and for a spacetime endowed with only such a defect we obtain precisely the well known expression of energy per unit length. However for a pure spacetime dislocation the total gravitational energy is zero.