Derivation of Source-Free Maxwell and Gravitational Radiation Equations by Group Theoretical Methods

TL;DR

This paper derives source-free Maxwell-like and gravitational equations for arbitrary helicity using group theoretical methods, revealing their transformation properties and reducing to known equations for specific cases.

Contribution

It introduces a group theoretical derivation of source-free equations for any helicity, unifying electromagnetic and gravitational wave equations within a common framework.

Findings

Derived Maxwell-like equations for arbitrary helicity j

Reduced to standard Maxwell equations for j=1

Extended to gravitational analogs for j=2

Abstract

We derive source-free Maxwell-like equations in flat spacetime for any helicity "j" by comparing the transformation properties of the 2(2j+1) states that carry the manifestly covariant representations of the inhomogeneous Lorentz group with the transformation properties of the two helicity "j" states that carry the irreducible representations of this group. The set of constraints so derived involves a pair of curl equations and a pair of divergence equations. These reduce to the free-field Maxwell equations for j=1 and the analogous equations coupling the gravito-electric and the gravito-magnetic fields for j=2.