Mathematicians from RUDN University analyzed the properties of gravitational waves in a generalized affine-metric space (an algebraic construction acting on the concepts of a vector and a point) - similar to the properties of electromagnetic waves in Minkowski space. They reported on the possibility of spatial transmission of information using non-metric waves without distortion. The discovery could provide new ways of transferring data in space - for example, between space stations. The research results are published in the journal Classical and Quantum Gravity.
Gravitational waves are waves in the curvature of space-time, which, according to General Relativity (GTR), are completely determined by space-time itself. There are several reasons to think of spacetime as a more complex structure with additional geometric characteristics such as twisting and non-metricity. In this case, speaking in the language of geometry, the space-time is transformed from the Riemannian space provided for by general relativity into the generalized affine-metric space. The corresponding equations of the gravitational field, generalizing Einstein's equations, show that twist and non-metricity can also propagate in the form of waves - in particular, in the form of plane waves over long distances from their sources.
To describe gravitational waves, researchers from RUDN University used mathematical abstraction - affine space, that is, an ordinary vector space, but without a source of coordinates. They proved that in such a mathematical representation of gravitational waves, there are functions that remain unchanged during the propagation of waves. You can configure an arbitrary function to encrypt any information in much the same way that electromagnetic waves transmit radio signals.
Information can be transmitted through space without distortion using non-metric waves.
If scientists can develop a method to incorporate these structures into a wave source, they will reach any point in space without any changes. That is, gravitational waves can be used to transmit data.
The study consisted of three stages. First, mathematicians calculated the Lie derivative - a function that relates the properties of bodies in two different spaces: an affine space and a Minkowski space. This allowed scientists to move from describing waves in real space to their mathematical interpretation.
Then they defined five arbitrary functions of time, that is, structures that do not change as the wave propagates. With their help, the characteristics of the wave can be placed in the source, thereby encrypting any information. It can be decoded at any point in space, that is, it can be transmitted.
At the third stage, the researchers proved the theorem on the structure of flat non-metricity in gravitational waves. It turned out that three out of four wave dimensions (three spatial and one temporal) can be used to encrypt an information signal using one function, and in the fourth dimension - using two.
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“We found that non-metric waves are capable of transmitting data like recently discovered waves of curvature, since their description contains arbitrary functions of delayed time, which can be encoded into the source of such waves,” explains Nina Markova, co-author of the study, Ph. D. in physics and mathematics, assistant professor Of the Mathematical Institute S. M. Nikolsky and an employee of the RUDN University.
