Space-time defects :Domain walls and torsion

TL;DR

This paper derives exact static thin domain wall solutions in Einstein-Cartan gravity using distribution theory, revealing curvature and torsion singularities, and explores the global structure of nonstatic torsion walls.

Contribution

It introduces new exact solutions for domain walls in Einstein-Cartan theory and analyzes their singularity structures and global properties.

Findings

Curvature δ-singularities are present in static solutions.

Cartan torsion exhibits Heaviside function behavior.

Weitzenböck planar walls have torsion δ-singularities and zero curvature.

Abstract

The theory of distributions in non-Riemannian spaces is used to obtain exact static thin domain wall solutions of Einstein-Cartan equations of gravity. Curvature $ \delta $-singularities are found while Cartan torsion is given by Heaviside functions. Weitzenb\"{o}ck planar walls are caracterized by torsion $\delta$-singularities and zero curvature. It is shown that Weitzenb\"{o}ck static thin domain walls do not exist exactly as in general relativity. The global structure of Weitzenb\"{o}ck nonstatic torsion walls is investigated.