# American Institute of Mathematical Sciences

May  2012, 17(3): 835-848. doi: 10.3934/dcdsb.2012.17.835

## Gravitational and electromagnetic properties of almost standing fields

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Received  June 2011 Revised  July 2011 Published  January 2012

For a scalar field propagating at light velocity $c$, kinematic properties of standing waves with constant frequency $\omega{}$ and velocity $v$, are formally identical with mechanic properties of isolated matter. They are both described by equations with the same mathematical structure, expressed by the Lorentz transformation with constant velocities $c$ and $v$. For almost standing waves, the variations of constant quantities lead to their dynamic properties. When they arise from adiabatic variations of the frequency $\Omega(x,t) = \omega \pm \delta\Omega(x,t)$, with $\omega{}$ constant, and $\delta\Omega(x,t) \ll \omega{}$, they lead to interactions which are formally identical with electromagnetic interactions. When they derive from variations of the field velocity $C(x,t) = c \pm \delta C(x,t)$, with $c$ constant, and $\delta C(x,t) \ll c$, they lead to interactions which are formally identical with gravitational interactions. The correspondence between almost standing waves of the field and matter, offers a common frame allowing an approach to investigate how gravitational and electromagnetic properties articulate together.
Citation: Claude Elbaz. Gravitational and electromagnetic properties of almost standing fields. Discrete & Continuous Dynamical Systems - B, 2012, 17 (3) : 835-848. doi: 10.3934/dcdsb.2012.17.835
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