Energy density in Rainbow Gravity: Levi-Civita Model

In this study, the energy density for the Levi-Civita space-time is analyzed within the framework of Rainbow Gravity Theory (RGT). RGT is a theoretical approach that assumes the geometry of space-time depends on the energy of the test particle, offering a promising perspective in the quest for quantum gravity. Energy densities are calculated using the Einstein, Bergmann-Thomson, and Landau-Lifshitz energy-momentum prescriptions and compared with the results obtained from General Relativity. The findings reveal that as the test particle’s energy increases, the energy density rises in the Einstein and Landau-Lifshitz prescriptions, while it decreases in the Bergmann-Thomson formulation. This highlights how the problem of energy localization varies across different energy-momentum definitions and demonstrates the impact of RGT on energy distribution. The study contributes to the literature exploring the influence of alternative gravitational theories on energy-momentum distributions.