Spherically symmetric Weitzenb\"{o}ck defect solution of Einstein field equation

TL;DR

This paper introduces a new class of spherically symmetric spacetime defect solutions within Einstein's field equations, characterized by a core with torsion but no curvature, and a vacuum exterior with topological defects.

Contribution

It presents a novel solution in Poincaré Gauge Field theory that describes spacetime defects with unique torsion and curvature properties, expanding the understanding of gravitational defects.

Findings

Core region has nonvanishing torsion but zero curvature.

Exterior region is vacuum with zero curvature and torsion.

Solution indicates the presence of weak Tachyonic effects far from the defect core.

Abstract

A new class of spacetime defect solutions of Einstein Field equations of Edelen's direct Poincar\'{e} Gauge Field theory without biaxial symmetry is presented. The interior solution describes a core of defects where curvature vanishes and Cartan torsion is nonvanishing. Outside the core (in vacuum) the solution represents a spacetime with vanishing curvature and torsion describing a nontrivial topological defect solution of Einstein equations of gravity. Our solution corresponds to a very weak strenght of Tachyons can be found far away from the core defect.