On metric-invariant relativistic transformations under anisotropy in the context of special relativity

Abstract

In a context of special relativity under anisotropy, Burde recently presented in this journal a new group of coordinate transformations obtained using Lie group techniques from the principles of relativity and correspondence, which show conformal metric invariance. As a consequence, this author argued that conformal invariance is a necessary condition of any anisotropic transformation satisfying those principles, and rejected the adequacy of any transformation obtained from the Lorentz transformation by a coordinate change, e.g. resynchronization such as the [Formula: see text]-Lorentz transformation. This paper argues against these assertions, and presents, as a counterexample, a relativistic generalization of the Tangherlini transformation obtained by the same Lie group method, that satisfies the previous requirements and enjoys the metric invariance property.