On Equations for a Spin-2 Particle in External Gravitational Field

TL;DR

This paper generalizes a first-order, 30-component wave equation for a spin-2 particle to include external electromagnetic fields and curved spacetime, maintaining covariance and eliminating lower spin components from the outset.

Contribution

It introduces a generally covariant first-order wave equation for spin-2 particles in external fields, preserving the Pauli-Fierz framework and ensuring the removal of lower spin states from the initial formulation.

Findings

Derived a covariant wave equation for spin-2 particles in external fields.

Ensured the elimination of spin 0 and 1 components at the equation's start.

Maintained equivalence to the second-order Pauli-Fierz equation.

Abstract

30-component, of the first order, equation for a spin 2 particle, equivalent to the second order Pauli-Fierz one, is generalized to presence of an external electromagnetic field as well as a curved background space-time geometry. The essential property of the generally covariant wave equation obtained is that here from the very beginning, in accordance with requirement of the Pauli-Fierz approach, a set of additional relations on 30-component wave function for eliminating complementary spin 0 and spin 1 fields is present at the starting equation.