Einstein gravity with torsion induced by the scalar field

TL;DR

This paper explores Einstein gravity with torsion coupled to a conformal scalar field in 2+1 dimensions, solving the complex equations numerically and deriving analytical solutions for the scalar field in asymptotic regions.

Contribution

It introduces a numerical approach to Einstein gravity with torsion coupled to a scalar field and derives analytical solutions for the scalar field at large distances.

Findings

Numerical solutions obtained using 4th order Runge-Kutta method.

Analytical scalar field solutions derived for asymptotic regions.

Proposed an ansatz for the rotation parameter in the metric.

Abstract

We couple a conformal scalar field in (2+1) dimensions to Einstein gravity with torsion. The field equations are obtained by a variational principle. We could not solve the Einstein and Cartan equations analytically. These equations are solved numerically with 4th order Runge-Kutta method. From the numerical solution, we make an ansatz for the rotation parameter in the proposed metric, which gives an analytical solution for the scalar field for asymptotic regions.