Distinguishing between Kerr and rotating JNW space-times via frame dragging and tidal effects

Abstract

In this paper, we first investigate some aspects of frame dragging in strong gravity. The computations are carried out for the Kerr black hole and for the rotating Janis-Newman-Winicour solution, that is known to have a naked singularity on a surface at a finite radius. For the Kerr metric, a few interesting possibilities of gyroscope precession frequency, as measured by a Copernican observer outside the ergoregion, are pointed out. It is shown that for certain angular velocities of a stationary observer, this frequency might vanish exactly, close to the ergoregion. Similar computations are repeated for static observers in the naked singularity background, and strong enhancement of the Lense-Thirring precession frequency compared to the black hole case is established. Then, we study the nature of tidal forces in the rotating naked singularity background, in Fermi normal coordinates. Here, physical quantities characterizing tidal disruptions of celestial objects in equatorial circular orbits are computed numerically. Our results here indicate that there might be significant deviations from corresponding Kerr black hole calculations, up to the level of approximation that we consider. *

Tidal effects away from the equatorial plane in Kerr backgrounds

“…At this limit, the star surface at (q 1 s , q 2 s , 0) begins to form a cusp. Therefore, at Roche limit [22] (r…”

“…The size of the star is assumed to be smaller than the size of the cube so that on the surface of the star, the potential can be approximated to − R0 0 ρ d 3 q rq , where r q is the radial distance from the center, and R 0 is the average radius of the star. Since ρ is anyway zero outside the star, we can re-write the integral as − cube ρ d 3 q rq to simplify the computation [22].…”

“…q rq , where r q is the radial distance from the center, and R 0 is the average radius of the star. Since ρ is anyway zero outside the star, we can re-write the integral as − cube ρ d 3 q rq to simplify the computation[22]. The next step is to find out different constants of the problem using the recently obtainedφ.…”

Comment on “Can accretion disk properties observationally distinguish black holes from naked singularities?”

“…[4] (dealing with lensing effects), and also recently in Ref. [5] (dealing with frame dragging and tidal effects). However, any scalar metric that solves (1) should also satisfy the Klein-Gordon equation…”

“…Thence, Eq. ( 6) is not solved by (5) with the metric (2). Therefore, the metric (2) cannot solve (1) with the scalar (5).…”