New non-linear modified massless Klein–Gordon equation

2017/07/06 by Felipe A. Asenjo, Sergio A. Hojman
Mathematics · Physics and Astronomy · #Classical mechanics #Coupling (piping) #Current (fluid) #Geodesic #Klein–Gordon equation #Massless particle #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear system #Null (SQL) #Physics #Quantum Electrodynamics and Casimir Effect #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics #Quantum electrodynamics #Quantum mechanics #gr-qc

paper · pdf · doi:10.1140/epjc/s10052-017-5330-7

arxiv created 2017/07/06 · openalex publication_date 2017/11/01 · arxiv updated 2017/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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 60 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.

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