| Summary: | In this paper, it is shown that the super-potential defined by Einstein, Landau–Lifshitz, and Bergmann–Thompson in general relativity theory and in teleparallel gravity theory are equivalent for a general diagonal space–time metric. Therefore, the energy–momentum tensor defined by Einstein, Landau–Lifshitz, and Bergmann–Thompson is equivalent in general relativity theory and in teleparallel gravity theory for the general diagonal space–times. Two different examples are also given to ensure the validity of the established statements. However, this fact is not true in general for the non-diagonal space–times. Non-diagonal Phantom black hole metric and non-diagonal stationary axi-symmetric space–time are introduced as a counter-examples to prove the non-equivalence of the super-potential and energy–momentum tensor defined in general relativity theory and in teleparallel gravity theory.
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