Teleparallel Energy Density within the Framework of Rainbow Gravitation Theory for A Spatial Self-Similar, Local Rotational Symmetric Model

It is known that the general theory of relativity provides valuable answers about our universe. General relativity theory is used to describe space, time, and mass-energy interactions, while quantum theory is used to explain the behavior and interactions of microscopic particles. The gap between these two theories reveals the need to develop a unified theory of "quantum gravity". However, so far no universal theory has yet been found that fully resolves this conflict. This is a big puzzle that physicists have been working on for a long time, and unifying these two theories harmoniously is one of the biggest challenges in modern physics. One of the theories put forward for this purpose is the "Rainbow" theory of gravity. In this study, Einstein, Bergmann-Thomson and Landau-Lifshitz energy densities are calculated for a spatial self-similar, locally rotationally symmetric model using teleparallel geometry within the framework of the Rainbow theory of gravity. However, the results obtained are evaluated using rainbow functions that are well known in the literature. The obtained results are rewritten as explicit forms of energy densities for Einstein, Bergman-Thomson and Landau-Liftshitz representations using f_1 (\\chi)=1/(1-\\chi)and f_2 (\\chi)=1 rainbow functions. Accordingly, it has been shown that the test particle changes its energy density for the Einstein and Bergmann-Thomson energy-momentum prescriptions but does not change the energy density for the Landau-Liftshitz energy-momentum prescription.