Borislavov Vasilea, TeodorRuiz Cembranos, José AlbertoGigante Valcarcel, JorgeMartín Moruno, María Del Prado2023-06-172023-06-172017-11-101434-604410.1140/epjc/s10052-017-5331-6https://hdl.handle.net/20.500.14352/18600© The Author(s) 2017. The authors acknowledge Y. N. Obukov for useful discussions. This work was partly supported by the projects FIS2014-52837-P (Spanish MINECO) and FIS2016-78859-P (AEI/FEDER, UE), and Consolider-Ingenio MULTIDARK CSD2009- 00064. PMM was funded by MINECO through the postdoctoral training contract FPDI-2013-16161 during part of this work.We revisit the definition and some of the characteristics of quadratic theories of gravity with torsion. We start from a Lagrangian density quadratic in the curvature and torsion tensors. By assuming that General Relativity should be recovered when the torsion vanishes and investigating the behaviour of the vector and pseudo-vector 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.engAtribución 3.0 Españahttps://creativecommons.org/licenses/by/3.0/es/journal articlehttp://dx.doi.org/10.1140/epjc/s10052-017-5331-6https://link.springer.comhttps://arxiv.org/abs/1706.07080open access53free gravity lagrangiansPoincare Gauge-theoryGeneral-ralativityPropagating torsionBirkhoff theoremGauss-BonnetSpace-time.Física-Modelos matemáticos