On the (non-)uniqueness of the Levi-Civita solution in the Einstein–Hilbert–Palatini formalism Bernal, Antonio N. Janssen, Bert Jiménez-Cano, Alejandro Orejuela, José Alberto Sánchez, Miguel Sánchez Moreno, Pablo Dynamics of a particle Differentiable dynamical systems Mathematics Physics We study the most general solution for affine connections that are compatible with the variational principle in the Palatini formalism for the Einstein–Hilbert action (with possible minimally coupled matter terms). We find that there is a family of solutions generalising the Levi-Civita connection, characterised by an arbitrary, non-dynamical vector field AμAμ. We discuss the mathematical properties and the physical implications of this family and argue that, although there is a clear mathematical difference between these new Palatini connections and the Levi-Civita one, both unparametrised geodesics and the Einstein equation are shared by all of them. Moreover, the Palatini connections are characterised precisely by these two properties, as well as by other properties of its parallel transport. Based on this, we conclude that physical effects associated to the choice of one or the other will not be distinguishable, at least not at the level of solutions or test particle dynamics. We propose a geometrical interpretation for the existence and unobservability of the new solutions. 2017-05-26T11:50:41Z 2017-05-26T11:50:41Z 2017-05-10 info:eu-repo/semantics/article Bernal, A.N.; et al. On the (non-)uniqueness of the Levi-Civita solution in the Einstein–Hilbert–Palatini formalism. Physics Letters B, 768: 280-287 (2017). [http://hdl.handle.net/10481/46542] 0370-2693 1873-2445 http://hdl.handle.net/10481/46542 10.1016/j.physletb.2017.03.001 eng http://creativecommons.org/licenses/by-nc-nd/3.0/ info:eu-repo/semantics/openAccess Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License Elsevier