Mathematical Formalism for an Experimental Test of Space-Time Anisotropy

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Gravitational Waves, General Relativity, Geodesy, Lorentz Transformation, Wave Equations, Gravitational Radiation, Magnetic Fields, And Other Observations, Classical General Relativity, Approximations, Special Relativity, Solutions Of Wave Equations: Bound States

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Some specific astrophysical data collected during the last decade suggest the need of a modification of the expression for the Einstein-Hilbert action, and several attempts are known in this respect. The modification suggested in this paper stems from a possible anisotropy of space-time-which leads to a dependence on directional variables of the simplest scalar in the least action principle. In order to provide a testable support to this idea, the optic-metrical parametric resonance is regarded-an experiment on a galactic scale, based on the interaction between the electromagnetic radiation of cosmic masers and periodical gravitational waves emitted by close double systems or pulsars. Since the effect depends on the space-time metric, a possible anisotropy could be revealed through observations. We prove that if space-time is anisotropic, then the orientation of the astrophysical systems suitable for observations would show it.

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