Search results for "quantum [statistics]"
showing 10 items of 4295 documents
Constraint preserving boundary conditions for the Z4c formulation of general relativity
2010
We discuss high order absorbing constraint preserving boundary conditions for the Z4c formulation of general relativity coupled to the moving puncture family of gauges. We are primarily concerned with the constraint preservation and absorption properties of these conditions. In the frozen coefficient approximation, with an appropriate first order pseudo-differential reduction, we show that the constraint subsystem is boundary stable on a four dimensional compact manifold. We analyze the remainder of the initial boundary value problem for a spherical reduction of the Z4c formulation with a particular choice of the puncture gauge. Numerical evidence for the efficacy of the conditions is prese…
The initial boundary value problem for free-evolution formulations of General Relativity
2017
We consider the initial boundary value problem for free-evolution formulations of general relativity coupled to a parametrized family of coordinate conditions that includes both the moving puncture and harmonic gauges. We concentrate primarily on boundaries that are geometrically determined by the outermost normal observer to spacelike slices of the foliation. We present high-order-derivative boundary conditions for the gauge, constraint violating and gravitational wave degrees of freedom of the formulation. Second order derivative boundary conditions are presented in terms of the conformal variables used in numerical relativity simulations. Using Kreiss-Agranovich-Metivier theory we demons…
Regularization of spherical and axisymmetric evolution codes in numerical relativity
2007
Several interesting astrophysical phenomena are symmetric with respect to the rotation axis, like the head-on collision of compact bodies, the collapse and/or accretion of fields with a large variety of geometries, or some forms of gravitational waves. Most current numerical relativity codes, however, can not take advantage of these symmetries due to the fact that singularities in the adapted coordinates, either at the origin or at the axis of symmetry, rapidly cause the simulation to crash. Because of this regularity problem it has become common practice to use full-blown Cartesian three-dimensional codes to simulate axi-symmetric systems. In this work we follow a recent idea idea of Rinne…
Locating ergostar models in parameter space
2020
Recently, we have shown that dynamically stable ergostar solutions (equilibrium neutron stars that contain an ergoregion) with a compressible and causal equation of state exist [A. Tsokaros, M. Ruiz, L. Sun, S. L. Shapiro, and K. Ury\=u, Phys. Rev. Lett. 123, 231103 (2019)]. These stars are hypermassive, differentially rotating, and highly compact. In this work, we make a systematic study of equilibrium models in order to locate the position of ergostars in parameter space. We adopt four equations of state that differ in the matching density of a maximally stiff core. By constructing a large number of models both with uniform and differential rotation of different degrees, we identify the p…
Solutions of the Einstein field equations for a bounded and finite discontinuous source, and its generalization: Metric matching conditions and jumpi…
2019
We consider the metrics of the General Relativity, whose energy-momentum tensor has a bounded support where it is continuous except for a finite step across the corresponding boundary surface. As a consequence, the first derivative of the metric across this boundary could perhaps present a finite step too. However, we can assume that the metric is ${\cal C}^1$ class everywhere. In such a case, although the partial second derivatives of the metric exhibit finite (no Dirac $\delta$ functions) discontinuities, the Dirac $\delta$ functions will still appear in the conservation equation of the energy-momentum tensor. As a consequence, strictly speaking, the corresponding metric solutions of the …
Magnetorotational Collapse of Supermassive Stars: Black Hole Formation, Gravitational Waves and Jets
2017
We perform MHD simulations in full GR of uniformly rotating stars that are marginally unstable to collapse. Our simulations model the direct collapse of supermassive stars (SMSs) to seed black holes (BHs) that can grow to become the supermassive BHs at the centers of quasars and AGNs. They also crudely model the collapse of massive Pop III stars to BHs, which could power a fraction of distant, long gamma-ray bursts (GRBs). The initial stellar models we adopt are $\Gamma = 4/3$ polytropes seeded with a dynamically unimportant dipole magnetic field (B field). We treat initial B-field configurations either confined to the stellar interior or extending out from the interior into the stellar ext…
GW170817, General Relativistic Magnetohydrodynamic Simulations, and the Neutron Star Maximum Mass
2017
Recent numerical simulations in general relativistic magnetohydrodynamics (GRMHD) provide useful constraints for the interpretation of the GW170817 discovery. Combining the observed data with these simulations leads to a bound on the maximum mass of a cold, spherical neutron star (the TOV limit): ${M_{\rm max}^{\rm sph}}\lesssim 2.74/\beta$, where $\beta$ is the ratio of the maximum mass of a uniformly rotating neutron star (the supramassive limit) over the maximum mass of a nonrotating star. Causality arguments allow $\beta$ to be as high as $1.27$, while most realistic candidate equations of state predict $\beta$ to be closer to $1.2$, yielding ${M_{\rm max}^{\rm sph}}$ in the range $2.16…
Magnetic Ergostars, Jet Formation and Gamma-Ray Bursts: Ergoregions versus Horizons
2020
We perform the first fully general relativistic, magnetohydrodynamic simulations of dynamically stable hypermassive neutron stars with and without ergoregions to assess the impact of ergoregions on launching magnetically--driven outflows. The hypermassive neutron stars are modeled by a compressible and causal equation of state and are initially endowed with a dipolar magnetic field extending from the stellar interior into its exterior. We find that, after a few Alfv\'en times, magnetic field lines in the ergostar (star that contains ergoregions) and the normal star have been tightly wound in both cases into a helical funnel within which matter begins to flow outward. The maximum Lorentz fac…
Simulating the magnetorotational collapse of supermassive stars: Incorporating gas pressure perturbations and different rotation profiles
2018
Collapsing supermassive stars (SMSs) with masses $M \gtrsim 10^{4-6}M_\odot$ have long been speculated to be the seeds that can grow and become supermassive black holes (SMBHs). We previously performed GRMHD simulations of marginally stable magnetized $\Gamma = 4/3$ polytropes uniformly rotating at the mass-shedding limit to model the direct collapse of SMSs. These configurations are supported entirely by thermal radiation pressure and model SMSs with $M \gtrsim 10^{6}M_\odot$. We found that around $90\%$ of the initial stellar mass forms a spinning black hole (BH) surrounded by a massive, hot, magnetized torus, which eventually launches an incipient jet. Here we perform GRMHD simulations o…
Outer boundary conditions for Einstein's field equations in harmonic coordinates
2007
We analyze Einstein's vacuum field equations in generalized harmonic coordinates on a compact spatial domain with boundaries. We specify a class of boundary conditions which is constraint-preserving and sufficiently general to include recent proposals for reducing the amount of spurious reflections of gravitational radiation. In particular, our class comprises the boundary conditions recently proposed by Kreiss and Winicour, a geometric modification thereof, the freezing-Psi0 boundary condition and the hierarchy of absorbing boundary conditions introduced by Buchman and Sarbach. Using the recent technique developed by Kreiss and Winicour based on an appropriate reduction to a pseudo-differe…