88 research outputs found
Constraint violation in free evolution schemes: Comparing the BSSNOK formulation with a conformal decomposition of the Z4 formulation
No full textAsymptotically null slices in numerical relativity
No full textEThOS - Electronic Theses Online ServiceGBUnited Kingdo
Asymptotically null slices in numerical relativity: mathematical analysis and spherical wave equation
No full textWe investigate the use of asymptotically null slices combined with stretching or compactification of the radial coordinate for the numerical simulation of asymptotically flat spacetimes. We consider a 1-parameter family of coordinates characterized by the asymptotic relation r ~ R1-n between the physical radius R and the coordinate radius r, and the asymptotic relation K ~ Rn/2-1 for the extrinsic curvature of the slices. These slices are asymptotically null in the sense that their Lorentz factor relative to stationary observers diverges as ? ~ Rn/2. While 1 < n ? 2 slices intersect {\mathscr I^+}, 0< n\le 1 slices end at i0. We carry out numerical tests with the spherical wave equation on Minkowski and Schwarzschild spacetimes. Simulations using our coordinates with 0 < n ? 2 achieve higher accuracy at a lower computational cost in following outgoing waves to a very large radius than using standard n = 0 slices without compactification. Power-law tails in Schwarzschild are also correctly represented
Critical phenomena in gravitational collapse with two competing massless matter fields
No full textIn the gravitational collapse of matter beyond spherical symmetry, gravitational waves are necessarily present. On the other hand, gravitational waves can collapse to a black hole even without matter. One might therefore wonder whether the interaction and competition between the matter fields and gravitational waves affect critical phenomena at the threshold of black hole formation. For a toy model for this, we study type II critical collapse with two matter fields in spherical symmetry, namely a scalar field and a Yang-Mills field. On their own, both display discrete self-similarity in type II critical collapse, and we can take either one of them as a toy model for gravitational waves. To our surprise, in numerical time evolutions, we find that, for sufficiently good fine-tuning, the scalar field always dominates on sufficiently small scales. We explain our results by the conjectured existence of a "quasidiscretely self-similar" (QSS) solution shared by the two fields, equal to the known Yang-Mills critical solution at infinitely large scales and the known scalar field critical solution (the Choptuik solution) at infinitely small scales, with a gradual transition from one field to the other. This QSS solution itself has only one unstable mode and so acts as the critical solution for any mixture of scalar field and Yang-Mills initial data.</p
Simulations of gravitational collapse in null coordinates. I. Formulation and weak-field tests in generalized Bondi gauges
No full textWe present a code for numerical simulations of the collapse of regular initial data to a black hole in null coordinates. We restrict to twist-free axisymmetry with scalar field matter. Our coordinates are
Constraint preserving boundary conditions for the Z4c formulation of general relativity
No full textWe 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 pseudodifferential 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 punctur
Simulations of gravitational collapse in null coordinates. II. : critical collapse of an axisymmetric scalar field
No full textWe present the first numerical simulations in null coordinates of the collapse of nonspherical regular initial data to a black hole. We restrict to twist-free axisymmetry, and reinvestigate the critical collapse of a nonspherical massless scalar field. We find that the Choptuik solution governing scalar field critical collapse in spherical symmetry persists when fine-tuning moderately nonspherical initial data to the threshold of black hole formation. The nonsphericity evolves as an almost-linear perturbation until the end of the self-similar phase, and becomes dominant only in the final collapse to a black hole. We compare with numerical results of Choptuik et al., Baumgarte, and Marouda et al., and conclude that they have been able to evolve somewhat more nonspherical solutions. Future work with larger deviations from spherical symmetry, and in particular vacuum collapse, will require a different choice of radial coordinate that allows the null generators to reconverge locally
Critical phenomena in the gravitational collapse of electromagnetic waves
No full textWe numerically investigate the threshold of black-hole formation in the gravitational collapse of electromagnetic waves in axisymmetry. We find approximate power-law scaling ρmax∼(η∗−η)−2γ of the maximum density in the time evolution of near-subcritical data with γ≃0.145, where η is the amplitude of the initial data. We directly observe approximate discrete self-similarity in near-critical time evolutions with a log-scale echoing period of Δ≃0.55. The critical solution is approximately the same for two families of initial data, providing some evidence of universality. Neither the discrete self-similarity nor the universality, however, are exact. We speculate that the absence of an exactly discrete self-similarity might be caused by the interplay of electromagnetic and gravitational wave degrees of freedom, or by the presence of higher-order angular multipoles, or both, and discuss implications of our findings for the critical collapse of vacuum gravitational waves
Critical phenomena in the collapse of quadrupolar and hexadecapolar gravitational waves
No full textWe report on numerical simulations of critical phenomena near the threshold of black hole formation in the collapse of axisymmetric gravitational waves in vacuum. We discuss several new features of our numerical treatment, and then compare results obtained from families of quadrupolar and hexadecapolar initial data. Specifically, we construct (nonlinear) initial data from quadrupolar and hexadecapolar, time-symmetric wavelike solutions to the linearized Einstein equations (often referred to as Teukolsky waves), and evolve these using a shock-avoiding slicing condition. While our degree of fine-tuning to the onset of black-hole formation is rather modest, we identify several features of the threshold solutions formed for the two families. Both threshold solutions appear to display an at least approximate discrete self-similarity with an accumulation event at the center, and the characteristics of the threshold solution for the quadrupolar data are consistent with those found previously by other authors. The hexadecapolar threshold solution appears to be distinct from the quadrupolar one, providing further support to the notion that there is no universal critical solution for the collapse of vacuum gravitational waves.17 pages, 14 figure
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