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. *
Abundance matching studies have shown that the average relationship between galaxy radius and dark matter halo virial radius remains nearly constant over many orders of magnitude in halo mass, and over cosmic time since about z = 3. In this work, we investigate the predicted relationship between galaxy radius re and halo virial radius Rh in the numerical hydrodynamical simulations Illustris and IllustrisTNG from z ∼ 0–3, and compare with the results from the abundance matching studies. We find that Illustris predicts much higher re/Rh values than the constraints obtained by abundance matching, at all redshifts, as well as a stronger dependence on halo mass. In contrast, IllustrisTNG shows very good agreement with the abundance matching constraints. In addition, at high redshift it predicts a strong dependence of re/Rh on halo mass on mass scales below those that are probed by existing observations. We present the predicted re/Rh relations from Illustris and IllustrisTNG for galaxies divided into star-forming and quiescent samples, and quantify the scatter in re/Rh for both simulations. Further, we investigate whether this scatter arises from the dispersion in halo spin parameter and find no significant correlation between re/Rh and halo spin. We investigate the paths in re/Rh traced by individual haloes over cosmic time, and find that most haloes oscillate around the median re/Rh relation over their formation history.
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