Hidden Consequence of Active Local Lorentz Invariance

TL;DR

This paper explores a hidden implication of active local Lorentz invariance, revealing an equivalence between different spacetime structures with various curvature and torsion configurations.

Contribution

It uncovers a previously unnoticed consequence of local Lorentz invariance hypothesis, linking multiple spacetime geometries through invariance principles.

Findings

Active local Lorentz invariance implies equivalence between diverse spacetime structures.

The hypothesis constrains the possible curvature and torsion configurations.

This reveals a hidden symmetry in the geometric formulation of spacetime.

Abstract

In this paper we investigate a hidden consequence of the hypothesis that Lagrangians and field equations must be invariant under active local Lorentz transformations. We show that this hypothesis implies in an equivalence between spacetime structures with several curvature and torsion possibilities.