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Slowly rotating black holes in the non-projectable Ho\v{r}ava-Lifshitz (HL) theory were studied recently in Phys.
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P. Hořava, Phys. Rev. D 79
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D. Blas, O. Pujolas, and S. Sibiryakov, JHEP 04
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Cited alongside, same era.
E. Barausse, T. Jacobson, and T.P. Sotiriou, Phys. Rev. D 83
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D. Blas and S. Sibiryakov, Phys. Rev. D 84
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E. Barausse and T.P. Sotiriou, Phys. Rev. Lett. 109
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