Geodesics around gravitational dislocations

TL;DR

This paper introduces a method for deriving spherically symmetric dislocation solutions in a Poincaré gauge theory of gravity, analyzing geodesics and revealing static, dynamic, and tachyonic sectors.

Contribution

It presents a novel technique for generating dislocation solutions with vanishing Cartan torsion in a gauge theory of gravity, including static and time-dependent cases.

Findings

Photons follow geodesics similar to electrons around dislocations in solids.

Static and dynamic dislocation solutions are provided.

Tachyonic sectors are identified in the theory.

Abstract

A technique for generating spherically symmetric dislocation solutions of a direct Poincar\'{e} gauge theory of gravity based on homogeneous functions which makes Cartan torsion to vanish is presented.Static space supported dislocation and time dependent solutions are supplied.Photons move along geodesics in analogy to geodesics described by electrons around dislocations in solid state physics.Tachyonic sectors are also found.