GravitationalWaves and Higgs-Like Potential from Alena Tensor

Alena Tensor is a recently discovered class of energy-momentum tensors that proposes a general equivalence of the curved path and geodesic for analyzed spacetimes which allows the analysis of physical systems in curvilinear, classical and quantum descriptions. In this paper it is shown that Alena Tensor is related to the Killing tensor K and describes the class of GR solutions G + Λ g = 2 Λ K. In this picture, it is not matter that imposes curvature, but rather the geometric symmetries, encoded in the Killing tensor, determine the way spacetime curves and how matter can be distributed in it. It was also shown, that Alena Tensor gives decomposition of energy-momentum tensor of the electromagnetic field using two null-vectors and in natural way forces the Higgs-like potential to appear. The obtained generalized metrics (covariant and contravariant) allow for further analysis of metrics for curved spacetimes with effective cosmological constant. The obtained solution can be also analyzed using conformal geometry tools. The calculated Riemann and Weyl tensors allow the analysis of purely geometric aspects of curvature, Petrov-type classification, and tracking of gravitational waves independently of the matter sources. The existing results for electromagnetism were also arranged and reformulated based on principle of least action, and the directions of generalization to all gauge fields were discussed. The article has been supplemented with a file containing a computational notebook used for symbolic derivations which may help in further analysis of this approach.