Slowly rotating black holes in Hořava-Lifshitz gravity

In a recent paper we claimed that there are no slowly rotating, stationary, axisymmetric black holes in the infrared limit of Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz gravity, provided that they are regular everywhere apart from the central singularity. Here we point out a subtlety in the relation between Einstein-\ae{}ther theory and the infrared limit of Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz gravity which was missed in our earlier derivation and drastically modifies our conclusion: our earlier calculations (which are otherwise technically correct) do not really imply that there are no slowly rotating black holes in Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz gravity, but that there are no slowly rotating black holes in the latter that are also solutions of Einstein-\ae{}ther theory and vice versa. That is, even though the two theories share the static, spherically symmetric solutions, there are no slowly rotating black holes that are solutions to both theories. We proceed to generate slowly rotating black-hole solutions in the infrared limit of Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz gravity, and we show that the configuration of the foliation-defining scalar remains the same as in spherical symmetry, thus these black holes are expected to possess a universal horizon.

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