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It is well known that the teleparallel equivalent of general relativityyields the same vacuum solutions as general relativity does, which ensures thatthis particular teleparallel model is in good agreement with experiments. Aless known result concerns the existence of a wider class of teleparallelmodels which also admits these solutions when the spacetime is diagonalizableby means of a coordinate change. However, it is stated in Ref. [Phys. Rev. D67, 044016 (2003).] that the teleparallel equivalent of general relativity isthe only teleparallel model which admits black holes. To show that thisstatement is not true, I prove the existence of this wider class by taking anapproach different from that of Ref. [Phys. Rev. D 19, 3524 (1979)].

Equivalent teleparallel theories in diagonalizable spacetimes: Comment on "Metric-affine approach to teleparallel gravity"