Chronology Protection of Rotating Black Holes in a Viable Lorentz-Violating Gravity

We study causal properties of the recently found rotating black-hole solution in the low-energy sector of Horava gravity as a viable Lorentz-violating (LV) gravity in four dimensions with the LV Maxwell field and a cosmological constant $\mathrm{\Lambda }(>-3\mathrm{/}{a}^2)$ for an arbitrary rotation parameter $a$. The region of non-trivial causality violation containing closed timelike curves is exactly the same as in the Kerr-Newman or the Kerr-Newman-(Anti-)de Sitter solution. Nevertheless, chronology is protected in the new rotating black hole because the causality violating region becomes physically inaccessible by exterior observers due to the new three-curvature singularity at its boundary that is topologically two-torus including the usual ring singularity at $(r,\theta )=(0,\pi \mathrm{/}2)$. As a consequence, the physically accessible region outside the torus singularity is causal everywhere.