arXiv subjects

Matthew W. Choptuik

Publications and source records attributed to Matthew W. Choptuik.

At least 37 records · Page 2Linked to original sources

arXiv2007

Final Fate of Subcritical Evolutions of Boson Stars

We present results from a study of Type I critical phenomena in the dynamics of general relativistic boson stars in spherical symmetry. The boson stars are modelled with a minimally coupled, massive complex field (with no explicit self-interaction), and are driven to the threshold of black hole formation via their gravitational interaction with an initially imploding pulse of massless scalar field. Using a distinct coordinate system, we reproduce previous results [1,2], including the scaling of the lifetime of near-critical configurations, as well as the fact that such configurations are well described as perturbed, one-mode-unstable boson stars. In addition, we make a detailed study of the long-time evolution of marginally subcritical configurations. Contrary to previous claims [1,2], we find that the end state in such cases does not involve dispersal of the bulk of the boson star field to large radial distances, but instead can be generically described by a stable boson star executing large amplitude oscillations. Furthermore we show that these oscillations can be largely identified as excitations of the fundamental mode associated with the final boson star, as computed in perturbation theory.

gr-qc↗

arXiv2007

Critical Behavior in the Gravitational Collapse of a Scalar Field with Angular Momentum in Spherical Symmetry

We study the critical collapse of a massless scalar field with angular momentum in spherical symmetry. In order to mimic the effects of angular momentum we perform a sum of the stress-energy tensors for all the scalar fields with the same eigenvalue, l, of the angular momentum operator and calculate the equations of motion for the radial part of these scalar fields. We have found that the critical solutions for different values of l are discretely self-similar (as in the original l=0 case). The value of the discrete, self-similar period, Delta_l, decreases as l increases in such a way that the critical solution appears to become periodic in the limit. The mass scaling exponent, gamma_l, also decreases with l.

gr-qc↗

arXiv2006

Adaptive Mesh Refinement for Coupled Elliptic-Hyperbolic Systems

We present a modification to the Berger and Oliger adaptive mesh refinement algorithm designed to solve systems of coupled, non-linear, hyperbolic and elliptic partial differential equations. Such systems typically arise during constrained evolution of the field equations of general relativity. The novel aspect of this algorithm is a technique of "extrapolation and delayed solution" used to deal with the non-local nature of the solution of the elliptic equations, driven by dynamical sources, within the usual Berger and Oliger time-stepping framework. We show empirical results demonstrating the effectiveness of this technique in axisymmetric gravitational collapse simulations. We also describe several other details of the code, including truncation error estimation using a self-shadow hierarchy, and the refinement-boundary interpolation operators that are used to help suppress spurious high-frequency solution components ("noise").

gr-qc↗

arXiv2003

Critical Phenomena in the Einstein-Massless-Dirac System

We investigate the general relativistic collapse of spherically symmetric, massless spin-1/2 fields at the threshold of black hole formation. A spherically symmetric system is constructed from two spin-1/2 fields by forming a spin singlet with no net spin-angular momentum. We study the system numerically and find strong evidence for a Type II critical solution at the threshold between dispersal and black hole formation, with an associated mass scaling exponent $γ~ 0.26$. Although the critical solution is characterized by a continuously self-similar (CSS) geometry, the matter fields exhibit discrete self-similarity with an echoing exponent $Δ~ 1.34$. We then adopt a CSS ansatz and reduce the equations of motion to a set of ODEs. We find a solution of the ODEs that is analytic throughout the solution domain, and show that it corresponds to the critical solution found via dynamical evolutions.

gr-qc↗

arXiv2002

Numerical evidence for `multi-scalar stars'

We present a class of general relativistic soliton-like solutions composed of multiple minimally coupled, massive, real scalar fields which interact only through the gravitational field. We describe a two-parameter family of solutions we call ``phase-shifted boson stars'' (parameterized by central density rho_0 and phase delta), which are obtained by solving the ordinary differential equations associated with boson stars and then altering the phase between the real and imaginary parts of the field. These solutions are similar to boson stars as well as the oscillating soliton stars found by Seidel and Suen [E. Seidel and W.M. Suen, Phys. Rev. Lett. 66, 1659 (1991)]; in particular, long-time numerical evolutions suggest that phase-shifted boson stars are stable. Our results indicate that scalar soliton-like solutions are perhaps more generic than has been previously thought.

gr-qc↗

arXiv2002

Black-hole threshold solutions in stiff fluid collapse

Numerical studies of the gravitational collapse of a stiff (P=rho) fluid have found the now familiar critical phenomena, namely scaling of the black hole mass with a critical exponent and continuous self-similarity at the threshold of black hole formation. Using the equivalence of an irrotational stiff fluid to a massless scalar field, we construct the critical solution as a scalar field solution by making a self-similarity ansatz. We find evidence that this solution has exactly one growing perturbation mode; both the mode and the critical exponent, gamma ~ 0.94, derived from its eigenvalue agree with those measured in perfect fluid collapse simulations. We explain why this solution is seen as a critical solution in stiff fluid collapse but not in scalar field collapse, and conversely why the scalar field critical solution is not seen in stiff fluid collapse, even though the two systems are locally equivalent.

gr-qc↗

arXiv2001

Fine Structure of Oscillons in the Spherically Symmetric $ϕ^4$ Klein-Gordon Model

We present results from a study of the fine structure of oscillon dynamics in the 3+1 spherically symmetric Klein-Gordon model with a symmetric double-well potential. We show that in addition to the previously understood longevity of oscillons, there exists a resonant (and critical) behavior which exhibits a time-scaling law. The mode structure of the critical solutions is examined, and we also show that the upper-bound to oscillon formation (in $r_0$ space) is either non-existent or higher than previously believed. Our results are generated using a novel technique for implementing non-reflecting boundary conditions in the finite difference solution of wave equations. The method uses a coordinate transformation which blue-shifts and ``freezes'' outgoing radiation. The frozen radiation is then annihilated via dissipation explicitly added to the finite-difference scheme, with very little reflection into the interior of the computational domain.

hep-ph↗

arXiv2001

Critical phenomena at the threshold of black hole formation for collisionless matter in spherical symmetry

We perform a numerical study of the critical regime at the threshold of black hole formation in the spherically symmetric, general relativistic collapse of collisionless matter. The coupled Einstein-Vlasov equations are solved using a particle-mesh method in which the evolution of the phase-space distribution function is approximated by a set of particles (or, more precisely, infinitesimally thin shells) moving along geodesics of the spacetime. Individual particles may have non-zero angular momenta, but spherical symmetry dictates that the total angular momentum of the matter distribution vanish. In accord with previous work by Rein et al, our results indicate that the critical behavior in this model is Type I; that is, the smallest black hole in each parametrized family has a finite mass. We present evidence that the critical solutions are characterized by unstable, static spacetimes, with non-trivial distributions of radial momenta for the particles. As expected for Type I solutions, we also find power-law scaling relations for the lifetimes of near-critical configurations as a function of parameter-space distance from criticality.

gr-qc↗

arXiv2001

Critical Phenomena Associated with Boson Stars

We present a brief synopsis of related work (gr-qc/0007039), describing a study of black hole threshold phenomena for a self-gravitating, massive complex scalar field in spherical symmetry. We construct Type I critical solutions dynamically by tuning a one-parameter family of initial data consisting of a boson star and a massless real scalar field, and numerically evolving this data. The resulting critical solutions appear to correspond to boson stars on the unstable branch, as we show via comparisons between our simulations and perturbation theory. For low-mass critical solutions, we find small ``halos'' of matter in the tails of the solutions, and these distort the profiles which otherwise agree with unstable boson stars. These halos seem to be artifacts of the collisions between the original boson stars and the massless fields, and do not appear to belong to the true critical solutions. From this study, it appears that unstable boson stars are unstable to dispersal (``explosion'') in addition to black hole formation. Given the similarities in macroscopic stability between boson stars and neutron stars, we suggest that similar phenomena could occur in models of neutron stars.

gr-qc↗

arXiv2000

Gravitational collapse in 2+1 dimensional AdS spacetime

We present results of numerical simulations of the formation of black holes from the gravitational collapse of a massless, minimally-coupled scalar field in 2+1 dimensional, axially-symmetric, anti de-Sitter (AdS) spacetime. The geometry exterior to the event horizon approaches the BTZ solution, showing no evidence of scalar `hair'. To study the interior structure we implement a variant of black-hole excision, which we call singularity excision. We find that interior to the event horizon a strong, spacelike curvature singularity develops. We study the critical behavior at the threshold of black hole formation, and find a continuously self-similar solution and corresponding mass-scaling exponent of approximately 1.2. The critical solution is universal to within a phase that is related to the angle deficit of the spacetime.

gr-qc↗

arXiv2000

Boson stars driven to the brink of black hole formation

We present a study of black hole threshold phenomena for a self-gravitating, massive complex scalar field in spherical symmetry. We construct Type I critical solutions dynamically by tuning a one-parameter family of initial data composed of a boson star and a massless real scalar field. The real field is used to perturb the boson star via a gravitational interaction which results in a {\em significant} transfer of energy. The resulting critical solutions, which show great similarity with unstable boson stars, persist for a finite time before dispersing or forming a black hole. We extend the stability analysis of Gleiser and Watkins [Nucl. Phys. B319, 733 (1989)], providing a method for calculating the radial dependence of boson star modes of nonzero frequency. We find good agreement between our critical solutions and boson star modes. For critical solutions less than 90% of the maximum boson star mass $M_{\rm max} \simeq 0.633 M_{Pl}^2/m$, a small halo of matter appears in the tail of the solution. This halo appears to be an artifact of the collision between the original boson star and the real field, and does not belong to the true critical solution. It seems that unstable boson stars are unstable to dispersal in addition to black hole formation. Given the similarity in macroscopic stability between boson and neutron stars, we suggest that neutron stars at or beyond the point of instability may also be unstable to explosion.

gr-qc↗

arXiv2000

Locating Boosted Kerr and Schwarzschild Apparent Horizons

We describe a finite-difference method for locating apparent horizons and illustrate its capabilities on boosted Kerr and Schwarzschild black holes. Our model spacetime is given by the Kerr-Schild metric. We apply a Lorentz boost to this spacetime metric and then carry out a 3+1 decomposition. The result is a slicing of Kerr/Schwarzschild in which the black hole is propagated and Lorentz contracted. We show that our method can locate distorted apparent horizons efficiently and accurately.

gr-qc↗

arXiv1999

Ultrarelativistic fluid dynamics

This is the first of two papers examining the critical collapse of spherically symmetric perfect fluids with the equation of state P = (Gamma -1)rho. Here we present the equations of motion and describe a computer code capable of simulating the extremely relativistic flows encountered in critical solutions for Gamma <= 2. The fluid equations are solved using a high-resolution shock-capturing scheme based on a linearized Riemann solver.

gr-qc↗

arXiv1999

Critical phenomena in perfect fluids

We investigate the gravitational collapse of a spherically symmetric, perfect fluid with equation of state P = (Gamma -1)rho. We restrict attention to the ultrarelativistic (``kinetic-energy-dominated'', ``scale-free'') limit where black hole formation is anticipated to turn on at infinitesimal black hole mass (Type II behavior). Critical solutions (those which sit at the threshold of black hole formation in parametrized families of collapse) are found by solving the system of ODEs which result from a self-similar ansatz, and by solving the full Einstein/fluid PDEs in spherical symmetry. These latter PDE solutions (``simulations'') extend the pioneering work of Evans and Coleman (Gamma = 4/3) and verify that the continuously self-similar solutions previously found by Maison and Hara et al for $1.05 < Gamma < 1.89 are (locally) unique critical solutions. In addition, we find strong evidence that globally regular critical solutions do exist for 1.89 < Gamma <= 2$, that the sonic point for Gamma_dn = 1.8896244 is a degenerate node, and that the sonic points for Gamma >Gamma_dn are nodal points rather than focal points as previously reported. We also find a critical solution for Gamma = 2, and present evidence that it is continuously self-similar and Type II. Mass-scaling exponents for all of the critical solutions are calculated by evolving near-critical initial data, with results which confirm and extend previous calculations based on linear perturbation theory. Finally, we comment on critical solutions generated with an ideal-gas equation of state.

gr-qc↗

arXiv1999

New Critical Behavior in Einstein-Yang-Mills Collapse

We extend the investigation of the gravitational collapse of a spherically symmetric Yang-Mills field in Einstein gravity and show that, within the black hole regime, a new kind of critical behavior arises which separates black holes formed via Type I collapse from black holes formed through Type II collapse. Further, we provide evidence that these new attracting critical solutions are in fact the previously discovered colored black holes with a single unstable mode.

gr-qc↗

arXiv1997

Instability of an "Approximate Black Hole"

We investigate the stability of a family of spherically symmetric static solutions in vacuum Brans-Dicke theory (with $ω=0$) recently described by van Putten. Using linear perturbation theory, we find one exponentially growing mode for every member of the family of solutions, and thus conclude that the solutions are not stable. Using a previously constructed code for spherically symmetric Brans-Dicke, additional evidence for instability is provided by directly evolving the static solutions with perturbations. The full non-linear evolutions also suggest that the solutions are black-hole-threshold critical solutions.

gr-qc↗

arXiv1996

Black Hole--Scalar Field Interactions in Spherical Symmetry

We examine the interactions of a black hole with a massless scalar field using a coordinate system which extends ingoing Eddington-Finkelstein coordinates to dynamic spherically symmetric-spacetimes. We avoid problems with the singularity by excising the region of the black hole interior to the apparent horizon. We use a second-order finite difference scheme to solve the equations. The resulting program is stable and convergent and will run forever without problems. We are able to observe quasi-normal ringing and power-law tails as well an interesting nonlinear feature.

gr-qc↗

arXiv1996

Black Hole Criticality in the Brans-Dicke Model

We study the collapse of a free scalar field in the Brans-Dicke model of gravity. At the critical point of black hole formation, the model admits two distinctive solutions dependent on the value of the coupling parameter. We find one solution to be discretely self-similar and the other to exhibit continuous self-similarity.

gr-qc↗