2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57280In this paper we scrutinize the so called Principle of Local Lorentz Invariance (\emph{PLLI}) that many authors claim to follow from the Equivalence Principle. Using rigourous mathematics we introduce in the General Theory of Relativity two classes of reference frames (\emph{PIRFs} and \emph{LLRF}$γ$\emph{s}) which natural generalizations of the concept of the inertial reference frames of the Special Relativity Theroy. We show that it is the class of the \emph{LLRF}$γ$\emph{s} that is associated with the \emph{PLLI.} Next we give a defintion of physically equivalent referefrence frames. Then, we prove that there are models of General Relativity Theory (in particular on a Friedmann universe) where the \emph{PLLI}is false. However our find is not in contradiction with the many experimental claims vindicating the \emph{PLLI}, because theses experiments do not have enough accuracy to detect the effect we found. We prove moreover that \emph{PIRFs}are not physically equivalent.This is a version of a paper originally published in Found. Phys.(2001) which includes a corrigenda published in Found. Phys. 32, 811-812 (2002)Mathematical Physicstext