Dynamical torsion gravity backgrounds

TL;DR

This paper derives field equations for torsion gravity theories using metric and contorsion tensors, and finds explicit solutions under various ansätze, highlighting issues with predictability due to arbitrary functions in solutions.

Contribution

It provides a direct formulation of torsion gravity field equations in metric and contorsion variables and finds explicit solutions for different spacetime geometries.

Findings

Some solutions have arbitrary functions in the contorsion tensor that do not affect geometry

The formulation avoids vierbein formalism by using Lagrange multipliers

Raises questions about the predictability of torsion gravity theories

Abstract

We write the field equations of torsion gravity theories and the N\oe ther identity they obey directly in terms of metric and contorsion tensor components expressed with respect to natural coordinates, i.e. without using vierbien but Lagrange multipliers. Then we obtain explicit solutions of these equations, under specific ans\"atze for the contorsion field, by assuming the metric to be respectively of the Bertotti-Robinson, pp-wave, Friedmann-Lema\^itre-Robertson-Walker or static spherically symmetric type. Among these various solutions we obtain some of them have their contorsion tensor depending on arbitrary functions that didn't influence their geometry. This raises question about the predictability of the theory.