Einstein gravity with torsion induced by the scalar field

Highlights: •Study of Einstein gravity with torsion nonminimally coupled with a scalar field. •Looking for solutions in (2+1) dimensions. •Obtaining analytical solutions for asymptotic cases with an ansatz. •Results appear consistent with literature. -- 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.