New criterion for direct black hole formation in rapidly rotating stellar collapse

We study gravitational collapse of rapidly rotating relativistic polytropes of the adiabatic index $\Gamma = 1.5$ and 2, in which the spin parameter $q \equiv J/M^{2} > 1$ where $J$ and $M$ are total angular momentum and gravitational mass, in full general relativity. First, analyzing initial distributions of the mass and the spin parameter inside stars, we predict the final outcome after the collapse. Then, we perform fully general relativistic simulations on assumption of axial and equatorial symmetries and confirm our predictions. As a result of simulations, we find that in contrast with the previous belief, even for stars with $q > 1$, the collapse proceeds to form a seed black hole at central region, and the seed black hole subsequently grows as the ambient fluids accrete onto it. We also find that growth of angular momentum and mass of the seed black hole can be approximately determined from the initial profiles of the density and the specific angular momentum. We define an effective spin parameter at the central region of the stars, $q_{c}$, and propose a new criterion for black hole formation as q_{c} \alt 1. Plausible reasons for the discrepancy between our and previous results are clarified.Comment: submitted to PR

Magnetohydrodynamics in full general relativity: Formulation and tests

A new implementation for magnetohydrodynamics (MHD) simulations in full general relativity (involving dynamical spacetimes) is presented. In our implementation, Einstein's evolution equations are evolved by a BSSN formalism, MHD equations by a high-resolution central scheme, and induction equation by a constraint transport method. We perform numerical simulations for standard test problems in relativistic MHD, including special relativistic magnetized shocks, general relativistic magnetized Bondi flow in stationary spacetime, and a longterm evolution for self-gravitating system composed of a neutron star and a magnetized disk in full general relativity. In the final test, we illustrate that our implementation can follow winding-up of the magnetic field lines of magnetized and differentially rotating accretion disks around a compact object until saturation, after which magnetically driven wind and angular momentum transport inside the disk turn on.Comment: 28 pages, to be published in Phys. Rev.

Gravitational waves from axisymmetrically oscillating neutron stars in general relativistic simulations

Gravitational waves from oscillating neutron stars in axial symmetry are studied performing numerical simulations in full general relativity. Neutron stars are modeled by a polytropic equation of state for simplicity. A gauge-invariant wave extraction method as well as a quadrupole formula are adopted for computation of gravitational waves. It is found that the gauge-invariant variables systematically contain numerical errors generated near the outer boundaries in the present axisymmetric computation. We clarify their origin, and illustrate it possible to eliminate the dominant part of the systematic errors. The best corrected waveforms for oscillating and rotating stars currently contain errors of magnitude $\sim 10^{-3}$ in the local wave zone. Comparing the waveforms obtained by the gauge-invariant technique with those by the quadrupole formula, it is shown that the quadrupole formula yields approximate gravitational waveforms besides a systematic underestimation of the amplitude of $O(M/R)$ where $M$ and $R$ denote the mass and the radius of neutron stars. However, the wave phase and modulation of the amplitude can be computed accurately. This indicates that the quadrupole formula is a useful tool for studying gravitational waves from rotating stellar core collapse to a neutron star in fully general relativistic simulations. Properties of the gravitational waveforms from the oscillating and rigidly rotating neutron stars are also addressed paying attention to the oscillation associated with fundamental modes

Gravitational Waves from Gravitational Collapse

Gravitational wave emission from the gravitational collapse of massive stars has been studied for more than three decades. Current state of the art numerical investigations of collapse include those that use progenitors with realistic angular momentum profiles, properly treat microphysics issues, account for general relativity, and examine non--axisymmetric effects in three dimensions. Such simulations predict that gravitational waves from various phenomena associated with gravitational collapse could be detectable with advanced ground--based and future space--based interferometric observatories.Comment: 68 pages including 13 figures; revised version accepted for publication in Living Reviews in Relativity (http://www.livingreviews.org