External symmetry in general relativity

TL;DR

This paper extends the concept of isometry transformations in general relativity to include local frame effects for spin fields, introducing external symmetry transformations that combine isometries with tetrad gauge changes, revealing new physical observables.

Contribution

It generalizes isometry transformations to include local frame effects for spin fields, defining external symmetries as combined isometries and gauge transformations, and explores their physical implications.

Findings

External symmetry transformations form a group locally isomorphic to isometries.

Generators of these symmetries include specific spin terms representing new observables.

Examples include generators of central, de Sitter, and anti-de Sitter symmetries in different gauges.

Abstract

We propose a generalization of the isometry transformations to the geometric context of the field theories with spin where the local frames are explicitly involved. We define the external symmetry transformations as isometries combined with suitable tetrad gauge transformations and we show that these form a group which is locally isomorphic with the isometry one. We point out that the symmetry transformations that leave invariant the equations of the fields with spin have generators with specific spin terms which represent new physical observables. The examples we present are the generators of the central symmetry and those of the maximal symmetries of the de Sitter and anti-de Sitter spacetimes derived in different tetrad gauge fixings. Pacs: 04.20.Cv, 04.62.+v, 11.30.-j