Slowly rotating black holes in Einstein-æther theory

We study slowly rotating, asymptotically flat black holes in Einstein-\ae{}ther theory and show that solutions that are free from naked finite area singularities form a two-parameter family. These parameters can be thought of as the mass and angular momentum of the black hole, while there are no independent \ae{} ther charges. We also show that the \ae{} ther has nonvanishing vorticity throughout the spacetime, as a result of which there is no hypersurface that resembles the universal horizon found in static, spherically symmetric solutions. Moreover, for experimentally viable choices of the coupling constants, the frame-dragging potential of our solutions only shows percent-level deviations from the corresponding quantities in General Relativity and Ho\ifmmode \check{r}\else \v{r}\fi{}ava gravity. Finally, we uncover and discuss several subtleties in the correspondence between Einstein-\ae{}ther theory and Ho\ifmmode \check{r}\else \v{r}\fi{}ava gravity solutions in the ${c}_{\ensuremath{\omega}}\ensuremath{\rightarrow}\ensuremath{\infty}$ limit.

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