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In this study, the energy–momentum localization problem is addressed within the framework of rainbow gravity. Considering the black string black hole, one of the cylindrical black hole models, energy–momentum distributions are obtained for Einstein, Bergmann–Thomson, and Landau–Liftshitz prescriptions in rainbow gravity. All prescriptions' energy densities are non-zero and depend on the rainbow functions, while the momentum distributions are zero. It has been observed that space-time energy does not depend on the energy of the test particle for some particular choices of rainbow functions. The results obtained for all special cases are given in a table. [ABSTRACT FROM AUTHOR]

Theoretical physicists generally prefer to modify the general theory of relativity rather than avoiding the successful approaches that have been offered to us. Hence, the rainbow formalism of gravity, which is one of the most studied quantum gravity candidates in literature, has recently gained importance in the field. In this study, the energy–momentum localization problem is discussed for the Taub universe within the framework of rainbow gravity. To achieve this goal, energy and momentum components are calculated by making use of diverse values of rainbow functions in the Einstein, Bergmann–Thomson, Landau–Lifshitz, and the Papapetrou prescriptions for the geometry under consideration. Except for the Landau–Lifshitz prescription, all prescriptions depend on the rainbow functions and the momentum components vanish. Graphical analysis is performed for all the energies obtained. Also, it is shown in limiting condition f 1 (χ) → 1 , f 2 (χ) → 1 that the results are compatible with the ones obtained in the general relativity. [ABSTRACT FROM AUTHOR]