Gravitational Waves from Alena Tensor

Alena Tensor is a recently discovered class of energy-momentum tensors that proposes a general equivalence of the curved path and the geodesic for the analyzed spacetimes which allows the analysis of physical systems in curvilinear, classical and quantum descriptions. In this paper it was shown that Alena Tensor gives decomposition of energy-momentum tensor of the electromagnetic field using two null-vectors. The discovery of the connection of the Alena Tensor with the Killing tensor shows that the energy-momentum tensor of matter can be expressed in terms of the Killing tensor. In this picture, it is not matter that imposes symmetry, but rather the geometric symmetries, encoded in the Killing tensor, determine the way spacetime curves and how matter can be distributed in it. In other words, it is geometry and its hidden symmetry that are the source of matter's structure. It was also shown, that Alena Tensor approach naturally leads to the existence of gravitational waves. The calculated Weyl tensor allows the analysis of purely geometric aspects of curvature, Petrov-type classification, and tracking of gravitational waves independently of the matter sources. The obtained generalized metric also allows for further analysis of metrics for curved spacetimes Petrov type D (and degenerated ones) with effective cosmological constant. A certain simplification of the analysis of gravitational waves has also been proposed, which may help both in their analysis and in the proof of the validity of the Alena Tensor. The article has been supplemented with the Alena Tensor equations with a positive value of the electromagnetic field tensor invariant (related to cosmological constant) which may help in further analysis of this approach.