Abstract:
Gravitational-wave emission from stellar collapse has been studied for nearly four decades. Current state-of-the-art numerical investigations of collapse include those that use progenitors with more 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 ground-based and space-based interferometric observatories. This review covers the entire range of stellar collapse sources of gravitational waves: from the accretion-induced collapse of a white dwarf through the collapse down to neutron stars or black holes of massive stars to the collapse of supermassive stars.

Abstract:
We demonstrate that evolutions of three-dimensional, strongly non-linear gravitational waves can be followed in numerical relativity, hence allowing many interesting studies of both fundamental and observational consequences. We study the evolution of time-symmetric, axisymmetric {\it and} non-axisymmetric Brill waves, including waves so strong that they collapse to form black holes under their own self-gravity. The critical amplitude for black hole formation is determined. The gravitational waves emitted in the black hole formation process are compared to those emitted in the head-on collision of two Misner black holes.

Abstract:
An axisymmetric collapse of non-rotating gravitational waves is numerically investigated in the subcritical regime where no black holes form but where curvature attains a maximum and decreases, following the dispersion of the initial wave packet. We focus on a curvature invariant with dimensions of length, and find that near the threshold for black hole formation it reaches a maximum along concentric rings of finite radius around the axis. In this regime the maximal value of the invariant exhibits a power-law scaling with the approximate exponent 0.38, as a function of a parametric distance from the threshold. In addition, the variation of the curvature in the critical limit is accompanied by increasing amount of echos, with nearly equal temporal and spatial periods. The scaling and the echoing patterns, and the corresponding constants, are independent of the initial data and coordinate choices.

Abstract:
The recent discovery of gravitational waves has revolutionized our understanding of many aspects regarding how the universe works. The formation of galaxies stands as one of the most challenging problems in astrophysics. Regardless of how far back we look in the early universe, we keep discovering galaxies with supermassive black holes lurking at their centers. Many models have been proposed to explain the rapid formation of supermassive black holes, including the massive accretion of material, the collapse of type III stars, and the merger of stellar mass black holes. Some of these events give rise to the production of gravitational waves that could be detected by future generations of more sensitive detectors. Alternatively, the existence of these supermassive black holes can be explained in the context of primordial black holes. In this paper we discuss the various models of galaxy formation shedding light on the role that gravitational waves can play to test of the validity of some of these models. We also discuss the prospect of primordial black holes as a seeding constituent for galaxy formation.

Abstract:
We provide details and present additional results on the numerical study of the gravitational-wave emission from the collapse of neutron stars to rotating black holes in three dimensions. More specifically, we concentrate on the advantages and disadvantages of the use of the excision technique and on how alternative approaches to that of excision can be successfully employed. Furthermore, as a first step towards source-characterization, we present a systematic discussion of the influence that rotation and different perturbations have on the waveforms and hence on the energy emitted in gravitational waves.

Abstract:
Superposition of gravitational waves generated by astrophysical sources is expected to give rise to the stochastic gravitational-wave background. We focus on the background generated by the ring-down of black holes produced in the stellar core collapse events across the universe. We systematically study the parameter space in this model, including the most recent information about the star formation rate and about the population of black holes as a function of redshift and of metallicity. We investigate the accessibility of this gravitational wave background to the upcoming gravitational-wave detectors, such as Advanced LIGO and Einstein Telescope.

Abstract:
Nonspherical stellar collapse to a black hole is one of the most promising gravitational wave sources for gravitational wave detectors. We numerically study gravitational waves from a slightly nonspherical stellar collapse to a black hole in linearized Einstein theory. We adopt a spherically collapsing star as the zeroth-order solution and gravitational waves are computed using perturbation theory on the spherical background. In this paper we focus on the perturbation of odd-parity modes. Using the polytropic equations of state with polytropic indices $n_p=1$ and 3, we qualitatively study gravitational waves emitted during the collapse of neutron stars and supermassive stars to black holes from a marginally stable equilibrium configuration. Since the matter perturbation profiles can be chosen arbitrarily, we provide a few types for them. For $n_p=1$, the gravitational waveforms are mainly characterized by a black hole quasinormal mode ringing, irrespective of perturbation profiles given initially. However, for $n_p=3$, the waveforms depend strongly on the initial perturbation profiles. In other words, the gravitational waveforms strongly depend on the stellar configuration and, in turn, on the ad hoc choice of the functional form of the perturbation in the case of supermassive stars.

Abstract:
We propose a scenario in which massive stars form at the outer edges of an AGN accretion disc. We analyze the dynamics of a disc forming around a supermassive black hole, in which the angular momentum is transported by turbulence induced by the disc's self-gravity. We find that once the surface density of the disc exceeds a critical value, the disc fragments into dense clumps. The biggest clumps collapse and form massive stars, which produce few-tens-solar-mass black holes at the end of their evolution. The embedded black holes will interact gravitationally with the massive accretion disc and be dragged towards the central black hole. Merger of a disc-born black hole with the central black hole will produce a burst of gravitational waves. If the central black hole is accreting at a rate comparable to the Eddington limit, the gas drag from the accretion disc will not alter significantly the dynamics of the final year of merger, and the gravitational waves should be observable by LISA. We argue that for a reasonable range of parameters such mergers will be detected monthly, and that the gravitational-wave signal from these mergers is distinct from that of other merger scenarios. Also, for some plausible black hole masses and accretion rates, the burst of gravitational waves should be accompanied by a detectable change in the optical luminosity of the central engine.

Abstract:
Gravitational wave bursts in the formation of neutron stars and black holes in energetic core-collapse supernovae (CC-SNe) are of potential interest to LIGO-Virgo and KAGRA. Events nearby are readily discovered using moderately sized telescopes. CC-SNe are competitive with mergers of neutron stars and black holes, if the fraction producing an energetic output in gravitational waves exceeds about 1\%. This opportunity motivates the design of a novel Sejong University Core-CollapsE Supernova Survey (SUCCESS), to provide triggers for follow-up searches for gravitational waves. It is based on the 76 cm Sejong University Telescope (SUT) for weekly monitoring of nearby star-forming galaxies, i.e., M51, M81-M82 and Blue Dwarf Galaxies from the Unified Nearby Galaxy Catalog with an expected yield of a few hundred per year. Optical light curves will be resolved for the true time-of-onset for probes of gravitational waves by broadband time-sliced matched filtering.

Abstract:
Observations of low frequency gravitational waves by the space-based LISA mission will open a new observational window on the early universe and the emergence of structure. LISA will observe the dynamical coalescence of massive black hole binaries at high redshifts, giving an unprecedented look at the merger history of galaxies and the reionization epoch. LISA will also observe gravitational waves from the collapse of supermassive stars to form black holes, and will map the spacetime in the central regions of galaxy cusps at high precision.