Spherically symmetric solution in a space-time with torsion

TL;DR

This paper derives a new exact spherically symmetric solution in Einstein-Cartan theory with torsion, revealing connections to wormholes and scalar fields, and suggests potential for discovering more solutions.

Contribution

It introduces a novel exact evolving solution with torsion in Einstein-Cartan theory, linking it to known wormhole and scalar field solutions, and explores avenues for additional solutions.

Findings

Solution describes a space-time with vanishing scalar curvature at large distances and times.

Reduces to a wormhole and a localized scalar field with torsion kink in static limits.

Provides evidence for the existence of more solutions in Einstein-Cartan theory.

Abstract

By using the method of group analysis, we obtain a new exact evolving and spherically symmetric solution of the Einstein-Cartan equations of motion, corresponding to a space-time threaded with a three-form Kalb-Ramond field strength. The solution describes in its more generic form, a space-time which scalar curvature vanishes for large distances and for large time. In static conditions, it reduces to a classical wormhole solution and to a exact solution with a localized scalar field and a torsion kink, already reported in literature. In the process we have found evidence towards the construction of more new solutions.