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

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.