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