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We study slowly rotating, asymptotically flat black holes in Einstein-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 ther charges. We also show that the 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 r rava gravity. Finally, we uncover and discuss several subtleties in the correspondence between Einstein-ther theory and Ho r rava gravity solutions in the c_ limit.
Barausse et al. (Tue,) studied this question.