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.
Highlights
It is well known that point structureless particles which move on arbitrary background gravitational fields follow geodesics according to the Equivalence Principle (EP) of General Relativity
The modified Klein–Gordon equation (19) leads to a modification of the massless Klein–Gordon equation even in flat spacetime. This behavior is due to the form of the new coupling term which is not usual in General Relativity, but it often appears in quantum mechanics
The Bohm potential has been extensively explored in quantum mechanics [48,49,50,51], solid state physics [52,53,54], and quantum plasmas [55,56,57,58]
Summary
It is well known that point structureless particles which move on arbitrary background gravitational fields follow geodesics according to the Equivalence Principle (EP) of General Relativity. The massless Klein–Gordon equation on a curved background is obtained by modifying the minimal coupling of matter to gravity in a conformal manner This procedure is known to produce scalar waves moving along null geodesics only for specific metric backgrounds [12]. One can wonder if there is possible a modification to the massless Klein–Gordon equation such that every scalar wave follows null geodesics in any curved background metric, such that kμkμ = 0 always Modifications of this equation have been studied using fractional derivatives [39] and numerically through its non-linear form [40,41,42], but not in the curved spacetime context. Thereby, the propagation of charged massless spinless (modified) Klein–Gordon fields follow null geodesics on any curved spacetime
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
