Classical Solutions of a Torsion Gravity from a Large N Matrix Model

TL;DR

This paper derives classical solutions with torsion in a gravity model from a large N matrix framework, exploring homogeneous, isotropic, and spherically symmetric spacetimes.

Contribution

It introduces a novel approach to classical gravity solutions with torsion derived from the IKKT matrix model, expanding the understanding of matrix model gravity.

Findings

Time-dependent solutions with homogeneity and isotropy analyzed.

Time-independent solutions with spherical symmetry studied.

Torsion degrees of freedom incorporated into classical solutions.

Abstract

Large N matrices can describe covariant derivatives in curved space. Applying this interpretation to the IKKT matrix model, the field equation of gravity is derived from the matrix equation of motion. We study classical solutions of this field equation with torsion degrees of freedom in empty spacetime. Time dependent solutions with homogeneity and isotropy, and time independent solutions with spherical symmetry are investigated under particular settings of torsions.