Consistent Gravitationally-Coupled Spin-2 Field Theory

TL;DR

This paper develops a consistent theory for a massless spin-2 field coupled to gravity, using a teleparallel framework where the field is represented by a vector in the translation algebra, avoiding issues of traditional approaches.

Contribution

It introduces a novel spin-2 field formulation based on teleparallel gravity, differing from the metric tensor approach and resolving known consistency problems.

Findings

Equivalent to the metric-based theory in flat space

Remains consistent when coupled with teleparallel gravity

Avoids traditional spin-2 field inconsistencies

Abstract

Inspired by the translational gauge structure of teleparallel gravity, the theory for a fundamental massless spin-2 field is constructed. Accordingly, instead of being represented by a symmetric second-rank tensor, the fundamental spin-2 field is assumed to be represented by a spacetime (world) vector field assuming values in the Lie algebra of the translation group. The flat-space theory naturally emerges in the Fierz formalism and is found to be equivalent to the usual metric-based theory. However, the gravitationally coupled theory, with gravitation itself described by teleparallel gravity, is shown not to present the consistency problems of the spin-2 theory constructed on the basis of general relativity.