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Slowly rotating black holes in Einstein-æther theory

We study slowly rotating, asymptotically flat black holes in Einstein-aether 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 aether charges. We also show that the aether has non-vanishing 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 Horava gravity. Finally, we uncover and discuss several subtleties in the correspondence between Einstein-aether theory and Horava gravity solutions in the $c_ω\to\infty$ limit.