A metric theory of gravity with torsion in extra-dimension

TL;DR

This paper proposes a gravity theory with a hidden extra dimension and torsion confined to it, leading to deviations from Einstein's equations and novel solutions like naked singularities and oscillatory cosmologies.

Contribution

It introduces a metric-dependent torsion in extra dimensions with constraints ensuring the extra dimension remains hidden, resulting in new gravitational solutions.

Findings

Positive mass solutions with naked singularities that resemble Schwarzschild at large distances

Discovery of oscillatory cosmological solutions avoiding singular big bang

Deviations from Einstein equations at the dynamical level

Abstract

We consider a theory of gravity with a hidden extra-dimension and metric-dependent torsion. A set of physically motivated constraints are imposed on the geometry so that the torsion stays confined to the extra-dimension and the extra-dimension stays hidden at the level of four dimensional geodesic motion. At the kinematic level, the theory maps on to General Relativity, but the dynamical field equations that follow from the action principle deviate markedly from the standard Einstein equations. We study static spherically symmetric vacuum solutions and homogeneous-isotropic cosmological solutions that emerge from the field equations. In both cases, we find solutions of significant physical interest. Most notably, we find positive mass solutions with naked singularity that match the well known Schwarzschild solution at large distances but lack an event horizon. In the cosmological context, we find oscillatory scenario in contrast to the inevitable, singular big bang of the standard cosmology.