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The Abraham Zelmanov Journal
The journal for General Relativity, gravitation and cosmology


HOME > ARCHIVES > 2010, volume 3, pages 25-70

Gravitational Waves and Gravitational Inertial Waves According to the General Theory of Relativity

Larissa Borissova


This research concerns gravitational waves and gravitational inertial waves, considered as waves of the curvature of space (space-time). It was produced using the mathematical apparatus of chronometric invariants, which, being the projections of the four-dimensional quantities onto the line of time and the spatial section of an observer, are physically observable quantities. The wave functions (d'Alembertian) of the chronometrically invariant (physically observable) projections Xij, Yijk, Ziklj of the Riemann-Christoffel curvature tensor are deduced. The conditions of the non-stationarity of the wave functions are taken into focus. It is shown that, even in the absence of the deformation of space (Dik = 0), the non-stationarity of the wave functions is possible. Four such cases were found, depending on the gravitational inertial force Fi and the rotation of space Aik: 1) Fi = 0, Aik = 0; 2) Fi = 0, Aik ≠ 0; 3) Fi ≠ 0, Aik = 0; 4) Fi ≠ 0, Aik ≠ 0. It was shown that in the first case, where Fi = 0 and Aik = 0, in emptiness, space is flat. If one of the quantities Fi and Aik differs from zero, the metric remains stationary in emptiness and in the medium. If both Fi and Aik are nonzero, the metric can be non-stationary in both emptiness and the medium, if the field Fi is vortical. The main conclusion is that it is not necessary that only the deformation of space be a source of gravitational waves and gravitational inertial waves. The waves can exist even in non-deforming spaces, if the gravitational inertial force Fi and the rotation of space Aik differ from zero, and the field Fi is vortical.

Ref:  The Abraham Zelmanov Journal, 2010, volume 3, pages 25-70

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