Circular geodesics of naked singularities in the Kehagias-Sfetsos metric of Hořava’s gravity

We discuss photon and test-particle orbits in the Kehagias-Sfetsos (KS) metric of Ho\ifmmode \check{r}\else \v{r}\fi{}ava's gravity. For any value of the Ho\ifmmode \check{r}\else \v{r}\fi{}ava parameter $\ensuremath{\omega}$, there are values of the gravitational mass $M$ for which the metric describes a naked singularity, and this is always accompanied by a vacuum ``antigravity sphere'' on whose surface a test particle can remain at rest (in a zero angular momentum geodesic), and inside which no circular geodesics exist. The observational appearance of an accreting KS naked singularity in a binary system would be that of a quasistatic spherical fluid shell surrounded by an accretion disk, whose properties depend on the value of $M$, but are always very different from accretion disks familiar from the Kerr-metric solutions. The properties of the corresponding circular orbits are qualitatively similar to those of the Reissner-Nordstr\"om naked singularities. When event horizons are present, the orbits outside the Kehagias-Sfetsos black hole are qualitatively similar to those of the Schwarzschild metric.

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