Abstract: The equation of gravitational-capillary waves of deep water can be represented in form of Einstein field equation in general theory of relativity. In this case, waves with a minimum speed on surface of water will be a physical model of gravitational waves with the speed of light.
Introduction
Attempts to estimate the speed of gravitational waves are much more than to measure. I am impressed by the estimates in which gravitational waves are some surface waves with dispersion, such as capillary or Rayleigh waves on surface of the water. Such waves as a special form of thermal motion were considered by Jacob Frenkel [1]. He was one of the first to look at the nucleus of an atom as a drop and describe its decay in terms of a capillary phenomenon. The first was Georgy Gamov [2].
If the model of surface phenomena turned out to be useful on a nuclear scale that is one and a half dozen orders of magnitude away from ours, then why not work the other way -- why not look at our bright baryon world as a film on the surface of the dark world. Then, by analogy with water, the velocity spectrum of surface gravitational waves will fit in the interval from 1*c to n*c, where n ~ 10^4. For water, at least this is the case - from 0.23 m/s to 1,500 m/s. The given assessment is based on similarity of analogies.
Model
The equation for speed of gravitational-capillary waves of deep water has the form:
The minimum speed of gravitational-capillary waves of deep water uw = 0.231 m/s at 20 C and atmospheric pressure is obtained using the following parameters:
Equation (1) can be converted to the form of the Einstein field equation in the general theory of relativity (2).
References
[1]. Frenkel, Y.I. (1975) Kinetic Theory of Liquids. Nauka, Leningrad.(VI. Surface and Allied Phenomena)
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