We study the causal structure of dynamical charged black holes, with a sufficient number of massless fields, using numerical simulations. Neglecting Hawking radiation, the inner horizon is a null Cauchy horizon and a curvature singularity due to mass inflation. When we include Hawking radiation, the inner horizon becomes spacelike and is separated from the Cauchy horizon, which is parallel to the out-going null direction. Since a charged black hole must eventually transit to a neutral black hole, we studied the neutralization of the black hole and observed that the inner horizon evolves into a space-like singularity, generating a Cauchy horizon which is parallel to the ingoing null direction. Since the mass function is finite around the inner horizon, the inner horizon is regular and penetrable in a general relativistic sense. However, since the curvature functions become trans-Planckian, we cannot say more about the region beyond the inner horizon, and it is natural to say that there is a "physical" space-like singularity. However, if we assume an exponentially large number of massless scalar fields, our results can be extended beyond the inner horizon. In this case, strong cosmic censorship and black hole complementarity can be violated. ‡ In this paper, we use the outer and inner horizons in a local sense, i.e. we will use "apparent" or "trapping" horizons [29].

Radio relics detected in the outskirts of galaxy clusters are thought to trace radioemitting relativistic electrons accelerated at cosmological shocks. In this study, using the cosmological hydrodynamic simulation data for the large-scale structure formation and adopting a diffusive shock acceleration (DSA) model for the production of cosmic-ray (CR) electrons, we construct mock radio and X-ray maps of simulated galaxy clusters that are projected in the sky plane. Various properties of shocks and radio relics, including the shock Mach number, radio spectral index and luminosity are extracted from the synthetic maps and compared with observations. A substantial fraction of radio and X-ray shocks identified in these maps involve multiple shock surfaces along line of sights (LoSs), and the morphology of shock distributions in the maps depends on the projection direction. Among multiple shocks in a given LoS, radio observations tend to pick up stronger shocks with flatter radio spectra, while X-ray observations preferentially select weaker shocks with larger kinetic energy flux. As a result, the shock Mach numbers and locations derived from radio and X-ray observations could differ from each other in some cases. We also find that the distributions of the spectral index and radio power of the synthetic radio relics are somewhat inconsistent with those of observed real relics; a bit more radio relics have been observed closer to the cluster core and with steeper spectral indices. We suggest the inconsistency could be explained, if very weak shocks with M s 2 accelerate CR electrons more efficiently, compared to the DSA model adopted here.

Abstract:The Horizon Run 4 is a cosmological N -body simulation designed for the study of coupled evolution between galaxies and large-scale structures of the Universe, and for the test of galaxy formation models. Using 6300 3 gravitating particles in a cubic box of L box = 3150 h −1 Mpc, we build a dense forest of halo merger trees to trace the halo merger history with a halo mass resolution scale down to M s = 2.7 × 10 11 h −1 M ⊙ . We build a set of particle and halo data, which can serve as testbeds for comparison of cosmological models and gravitational theories with observations. We find that the FoF halo mass function shows a substantial deviation from the universal form with tangible redshift evolution of amplitude and shape. At higher redshifts, the amplitude of the mass function is lower, and the functional form is shifted toward larger values of ln(1/σ). We also find that the baryonic acoustic oscillation feature in the two-point correlation function of mock galaxies becomes broader with a peak position moving to smaller scales and the peak amplitude decreasing for increasing directional cosine µ compared to the linear predictions. From the halo merger trees built from halo data at 75 redshifts, we measure the half-mass epoch of halos and find that less massive halos tend to reach half of their current mass at higher redshifts. Simulation outputs including snapshot data, past lightcone space data, and halo merger data are available at http://sdss.kias.re.kr/astro/Horizon-Run4 .

The outskirts of galaxy clusters are continuously disturbed by mergers and gas infall along filaments, which in turn induce turbulent flow motions and shock waves. We examine the properties of shocks that form within r 200 in sample galaxy clusters from structure formation simulations. While most of these shocks are weak and inefficient accelerators of cosmic rays (CRs), there are a number of strong, energetic shocks which can produce large amounts of CR protons via diffusive shock acceleration. We show that the energetic shocks reside mostly in the outskirts and a substantial fraction of them are induced by infall of the warm-hot intergalactic medium from filaments. As a result, the radial profile of the CR pressure in the intracluster medium is expected to be broad, dropping off more slowly than that of the gas pressure, and might be even temporarily inverted, peaking in the outskirts. The volume-integrated momentum spectrum of CR protons inside r 200 has the power-law slope of 4.25-4.5, indicating that the average Mach number of the shocks of main CR production is in the range of M s CR ≈ 3-4. We suggest that some radio relics with relatively flat radio spectrum could be explained by primary electrons accelerated by energetic infall shocks with M s 3 induced in the cluster outskirts.