Comment on Metric-affine approach to teleparallel gravity

It is well known that the teleparallel equivalent of general relativity yields the same vacuum solutions as general relativity does, which ensures that this particular teleparallel model is in good agreement with experiments. A lesser known result concerns the existence of a wider class of teleparallel models which also admits these solutions when the spacetime is diagonalizable by means of a coordinate change. However, it is stated by Obukhov and Pereira [Phys. Rev. D 67, 044016 (2003)] that the teleparallel equivalent of general relativity is the only teleparallel model which admits black holes. To show that this statement is not true, I present the result of Hayashi and Shirafuji [Phys. Rev. D 19, 3524 (1979)], which proves the existence of this wider class by showing the equivalence between two Lagrangians. It turns out that this equivalence also holds for plane-wave metrics. In addition, I update the constraints on the parameters of the teleparallel models.