Internal Symmetry of Space-Time Connections with Torsion

TL;DR

This paper introduces an internal symmetry in metric-compatible space-time connections with torsion, showing that all theories derived from the Hilbert-Einstein action are equivalent to general relativity under a specific gauge.

Contribution

It reveals a natural internal symmetry in torsion-inclusive connections, unifying various gravity theories with general relativity through gauge choices.

Findings

Identifies an internal symmetry in torsion space-time connections.

Demonstrates equivalence of all Hilbert-Einstein derived theories to general relativity.

Provides a gauge condition linking torsion theories to standard gravity.

Abstract

In this brief article an internal symmetry of a generic metric compatible space-time connection, metric and generalized volume element is introduced. The symmetry arises naturally by considering a space-time connection containing a generic torsion tensor, and would otherwise be missed in the absence of torsion. When the transformation is applied to the Hilbert-Einstein action it is shown that by a choice of gauge all possible field theories arising from the Hilbert-Einstein action are equivalent to the standard theory of gravity described by general relativity.