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

Abstract

We discuss photon and test-particle orbits in the Kehagias-Sfetsos (KS) metric. For any value of the Hořava parameter ω, 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 quasi-static 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-Nordström naked singularities. When event horizons are present, the orbits outside the Kehagias-Sfetsos black hole are qualitatively similar to those of the Schwarzschild metric.

Vertical stability of circular orbits in relativistic razor-thin disks

“…This result is in accordance with the expression obtained by Vogt and Letelier [19] for isotropic metrics and with the general expression presented in [26,28].…”

“…In order to avoid repulsive forces, we must consider only regions where (e ψ ) ,R > 0 [28]. Let us now focus on the vertical stability of timelike circular geodesics.…”

“…[25]). Radial stability can also be analyzed by the relativistic generalization of Rayleigh's criterion [26][27][28]. Concerning razorthin disks, extensive numerical studies of the dynamics of timelike geodesic motion were performed in a wide class of spacetimes, including not only razor-thin disks, but also rings surrounding black holes [29][30][31][32][33].…”

Perfect fluid tori orbiting Kehagias–Sfetsos naked singularities

“…The K-S naked singularity spacetimes were recently extensively studied, in particular the effective potential of the test particle motion and the circular geodesics were studied in [31], where a close similarity with properties of the circular geodesics of the Reissner-Nordström (RN) naked singularity spacetimes [32,33] has been demonstrated. The ultra-high-energy particle collisions in the deepest parts of the gravitational potential of K-S naked singularity spacetimes have been studied in [34].…”

“…A wide range of optical phenomena related to the innermost parts of Keplerian discs (direct and indirect images, spectral continuum of thermal radiation, and profiled spectral lines) had been exposed in [35]. For all of the considered phenomena related to the K-S naked singularities, an "antigravity" effect [31,35] plays a fundamental role; a similar situation has also been discovered in braneworld naked singularity spacetimes [36][37][38][39][40]. However, it seems to be different in comparison to the rotating Kerr naked singularity spacetimes [41][42][43][44][45][46][47][48]; for a detailed analysis of the magnetized thick discs see [49].…”