Ultra-high-energy collisions of particles in the field of near-extreme Kehagias-Sfetsos naked singularities and their appearance to distant observers

Abstract

We demonstrate that ultra-high-energy collisions of particles falling freely from rest at infinity can occur in the field of near-extreme Kehagias-Sfetsos naked singularities related to the Hořava gravity. However, the efficiency of escaping of created ultrarelativistic particles and the energy efficiency of the collisional process relative to distant observers are significantly lowered due to large gravitational redshift, which is substantially lower in comparison to those related to the collisions occurring close to the equatorial plane of near-extreme Kerr naked-singularity spacetimes. In the Kehagias-Sfetsos naked-singularity spacetimes, the energy efficiency relative to distant observers corresponds to the covariant energy of the colliding particles only. Finally, we demonstrate how the ultra-high-energy collisions are modified for charged particles if the Kehagias-Sfetsos naked singularities are immersed in a uniform magnetic field.

Perfect fluid tori orbiting Kehagias–Sfetsos naked singularities

“…In the Schwarzschild limit, ω → ∞, the Ricci scalar has the asymptotic behavior R ∼ 1/ω. More information can be found 2 in [34]. The physical singularity of the K-S spacetimes located at r = 0 is of a special character, as the metric coefficients g tt (r = 0) = g rr (r = 0) = 1 are finite there, while their radial derivatives are divergent.…”

“…Circular geodesics were studied for the K-S black hole spacetimes in [22,55] and for the K-S naked singularity spacetimes in [31,34,35]. We give a short summary of the properties of the circular geodesics in dependence on the parameter ωM 2 .…”

“…The properties of the K-S spacetimes are governed by the dimensionless parameter ωM 2 [31,34,35]. If the Hořava parameter ω is assumed fixed, then the gravitational mass parameter M governs the character of the K-S spacetimes.…”

“…This sphere radius also determines the location of the innermost limit on the existence of circular geodesics, corresponding to orbits with zero angular momentum and zero angular frequency [31,35]. The properties of the circular geodesics in the K-S naked singularity spacetimes are strongly determined by the dimensionless parameter ωM 2 [31,34,35]: as 0 < ωM 2 < (ωM 2 ) mso = 0.2811, stable circular orbits exist between the static sphere at radius r stat and infinity, while the spacetimes (ωM 2 ) mso < ωM 2 < (ωM 2 ) γ = 0.3849 are characterized by two separated regions of stable circular geodesics. The outer region extends between the inner marginally stable orbit at r isco and infinity and the inner one extends between the static radius r stat and the outer marginally stable orbit at r osco , unstable circular geodesics are located at r osco < r < r isco .…”

“…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].…”