We make a short comment on our new general relativity formulated on the Weitzenb\"ock space-time. The new general relativity considered here has one free parameter besides the Einstein constant κ. The total action is invariant under a class of local Lorentz transformations, besides being invariant under general coordinate and global Lorentz transformations. The consequences of this "restricted local Lorentz invariance" are studied.
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Hayashi et al. (1981) studied this question.
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