Eur. Phys. J. C (2017) 77: 732
https://doi.org/10.1140/epjc/s10052-017-5330-7

Regular Article - Theoretical Physics

New non-linear modified massless Klein–Gordon equation

¹ UAI Physics Center, Universidad Adolfo Ibáñez, Santiago, Chile
² Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Santiago, Chile
³ Departamento de Ciencias, Facultad de Artes Liberales, Universidad Adolfo Ibáñez, Santiago, Chile
⁴ Departamento de Física, Facultad de Ciencias, Universidad de Chile, Santiago, Chile
⁵ Centro de Recursos Educativos Avanzados, CREA, Santiago, Chile

^* e-mail: felipe.asenjo@uai.cl

Received: 29 June 2017
Accepted: 24 October 2017
Published online: 2 November 2017

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.