# Stability in quadratic torsion theories

## TL;DR

This paper analyzes the stability of quadratic gravity theories with torsion, deriving conditions for stability and explicitly formulating the field equations using the Palatini approach.

## Contribution

It provides a comprehensive stability analysis for quadratic torsion gravity theories and derives their field equations via the Palatini variational principle.

## Key findings

- Necessary conditions for stability are identified.
- Explicit gravitational field equations are obtained.
- Behavior of torsion fields in weak gravity is characterized.

## Abstract

We revisit the definition and some of the characteristics of quadratic theories of gravity with torsion. We start from the most general Lagrangian density quadratic in the curvature and torsion tensors. By assuming that General Relativity should be recovered when torsion vanishes and investigating the behaviour of the vector and pseudovector torsion fields in the weak-gravity regime, we present a set of necessary conditions for the stability of these theories. Moreover, we explicitly obtain the gravitational field equations using the Palatini variational principle with the metricity condition implemented via a Lagrange multiplier.