We study the collapse of rapidly rotating supermassive stars that may have formed in the early Universe. By self-consistently simulating the dynamics from the onset of collapse using three-dimensional general-relativistic hydrodynamics with fully dyn
amical spacetime evolution, we show that seed perturbations in the progenitor can lead to the formation of a system of two high-spin supermassive black holes, which inspiral and merge under the emission of powerful gravitational radiation that could be observed at redshifts z>10 with the DECIGO or Big Bang Observer gravitational-wave observatories, assuming supermassive stars in the mass range 10^4-10^6 Msol. The remnant is rapidly spinning with dimensionless spin a^*=0.9. The surrounding accretion disk contains ~10% of the initial mass.
We present a new three-dimensional general-relativistic hydrodynamic evolution scheme coupled to dynamical spacetime evolutions which is capable of efficiently simulating stellar collapse, isolated neutron stars, black hole formation, and binary neut
ron star coalescence. We make use of a set of adapted curvi-linear grids (multipatches) coupled with flux-conservative cell-centered adaptive mesh refinement. This allows us to significantly enlarge our computational domains while still maintaining high resolution in the gravitational-wave extraction zone, the exterior layers of a star, or the region of mass ejection in merging neutron stars. The fluid is evolved with a high-resolution shock capturing finite volume scheme, while the spacetime geometry is evolved using fourth-order finite differences. We employ a multi-rate Runge-Kutta time integration scheme for efficiency, evolving the fluid with second-order and the spacetime geometry with fourth-order integration, respectively. We validate our code by a number of benchmark problems: a rotating stellar collapse model, an excited neutron star, neutron star collapse to a black hole, and binary neutron star coalescence. The test problems, especially the latter, greatly benefit from higher resolution in the gravitational-wave extraction zone, causally disconnected outer boundaries, and application of Cauchy-characteristic gravitational-wave extraction. We show that we are able to extract convergent gravitational-wave modes up to (l,m)=(6,6). This study paves the way for more realistic and detailed studies of compact objects and stellar collapse in full three dimensions and in large computational domains. The multipatch infrastructure and the improvements to mesh refinement and hydrodynamics codes discussed in this paper will be made available as part of the open-source Einstein Toolkit.
We perform 3+1 general relativistic simulations of rotating core collapse in the context of the collapsar model for long gamma-ray bursts. We employ a realistic progenitor, rotation based on results of stellar evolution calculations, and a simplified
equation of state. Our simulations track self-consistently collapse, bounce, the postbounce phase, black hole formation, and the subsequent early hyperaccretion phase. We extract gravitational waves from the spacetime curvature and identify a unique gravitational wave signature associated with the early phase of collapsar formation.
The accurate modeling of gravitational radiation is a key issue for gravitational wave astronomy. As simulation codes reach higher accuracy, systematic errors inherent in current numerical relativity wave-extraction methods become evident, and may le
ad to a wrong astrophysical interpretation of the data. In this paper, we give a detailed description of the Cauchy-characteristic extraction technique applied to binary black hole inspiral and merger evolutions to obtain gravitational waveforms that are defined unambiguously, that is, at future null infinity. By this method we remove finite-radius approximations and the need to extrapolate data from the near zone. Further, we demonstrate that the method is free of gauge effects and thus is affected only by numerical error. Various consistency checks reveal that energy and angular momentum are conserved to high precision and agree very well with extrapolated data. In addition, we revisit the computation of the gravitational recoil and find that finite radius extrapolation very well approximates the result at $scri$. However, the (non-convergent) systematic differences to extrapolated data are of the same order of magnitude as the (convergent) discretisation error of the Cauchy evolution hence highlighting the need for correct wave-extraction.
Gravitational radiation is properly defined only at future null infinity ($scri$), but in practice it is estimated from data calculated at a finite radius. We have used characteristic extraction to calculate gravitational radiation at $scri$ for the
inspiral and merger of two equal mass non-spinning black holes. Thus we have determined the first unambiguous merger waveforms for this problem. The implementation is general purpose, and can be applied to calculate the gravitational radiation, at $scri$, given data at a finite radius calculated in another computation.
