Lorentz group in gravity theories

TL;DR

This paper argues that the Lorentz group should not be considered a gauge group in gravity theories, emphasizing that true gravity theories are translation gauge theories and critiquing the role of Lorentz connections.

Contribution

It clarifies the conceptual distinction between Lorentz and translation gauge theories in gravity, proposing that genuine gravity theories should focus on translation gauge symmetry.

Findings

Lorentz connection is an inertial force, not a gauge potential.

All three theories of the Geometrical Trinity are translation gauge theories.

Covariantization of teleparallel gravity is physically unnecessary.

Abstract

In this paper, it is argued that in gravity theories the local Lorentz group can not be considered as a gauge group in the sense of Yang-Mills theories, the Lorentz connection is not a gauge potential but an artificial force, the inertial force. A genuine gravity theory should be a translation gauge theory, though a unnormal gauge theory. All the three theories of the Geometrical Trinity of Gravity are translation gauge theories. A real gravity theory should get rid of "gauging" Lorentz group. The covariantization of the teleparallel gravity is not necessary physically.