Space-time Anisotropy: Mathematical Formalism and Possibility of an Observational Test

Astronomy and Astrophysics – Astronomy

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Some specific astrophysical data collected during the last decade cause a need of modifications in the expression of the Einstein-Hilbert action, and several attempts sufficing this need are known. Most of them deal with the direct (and in a sense arbitrary) modification of the "simplest scalar". In this paper, we investigate the situation when the metric of the space is anisotropic. This leads to a natural change of the simplest scalar in the least action principle, and we construct a possible anisotropic model of space-time with the help of the proposed specific mathematical formalism based on direction dependent metrics.
In order to give a testable support for this idea, the optic-metrical parametric resonance is regarded - an experiment on 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 reveal itself through observations.

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