New non-linear modified massless Klein--Gordon equation

TL;DR

This paper introduces a nonlinear modification of the massless Klein-Gordon equation that guarantees wave propagation strictly along null geodesics in any curved spacetime, addressing limitations of the classical equation.

Contribution

A novel nonlinear Klein-Gordon equation derived from a Lagrangian with current-current interaction, ensuring null geodesic wave propagation in curved backgrounds.

Findings

Ensures wave propagation strictly along null geodesics.

Derived from a Lagrangian with a self-coupling term.

Addresses tail development in solutions of the classical equation.

Abstract

The massless Klein--Gordon equation on arbitrary curved backgrounds allows for solutions which develop "tails" inside the light cone and, therefore, do not strictly follow null geodesics as discovered by DeWitt and Brehme almost sixty years ago. A modification of the massless Klein--Gordon equation is presented which always exhibits null geodesic propagation of waves on arbitrary curved spacetimes. This new equation is derived from a Lagrangian which exhibits current--current interaction. Its non--linearity is due to a self--coupling term which is related to the quantum mechanical Bohm potential.