Black hole critical behavior with the generalized BSSN formulation

Akbarian, Arman; Choptuik, Matthew W.

doi:10.1103/physrevd.92.084037

Cited by 34 publications

(68 citation statements)

References 42 publications

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“…Our values are also in good agreement with most previous numerical studies (e.g. [35]) as well as the values provided by [4,6,7], who found ∆ by casting the problem as an eigenvalue problem. Similarly, our values of the critical exponent agree well with previous numerical results, as well as the perturbative values found by [4].…”

Section: A Spherical Symmetrysupporting

confidence: 92%

Aspherical deformations of the Choptuik spacetime

Baumgarte

2018

Phys. Rev. D

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We perform dynamical and nonlinear numerical simulations to study critical phenomena in the gravitational collapse of massless scalar fields in the absence of spherical symmetry. We evolve axisymmetric sets of initial data and examine the effects of deviation from spherical symmetry. For small deviations we find values for the critical exponent and echoing period of the discretely selfsimilar critical solution that agree well with established values; moreover we find that such small deformations behave like damped oscillations whose damping coefficient and oscillation frequencies are consistent with those predicted in the linear perturbation calculations of Martín-García and Gundlach. However, we also find that the critical exponent and echoing period appear to decrease with increasing departure from sphericity, and that, for sufficiently large departures from spherical symmetry, the deviations become unstable and grow, confirming earlier results by Choptuik et.al.. We find some evidence that these growing modes lead to a bifurcation, similar to those reported by Choptuik et.al., with two centers of collapse forming on the symmetry axis above and below the origin. These findings suggest that nonlinear perturbations of the critical solution lead to changes in the effective values of the critical exponent, echoing period and damping coefficient, and may even change the sign of the latter, so that perturbations that are stable in the linear regime can become unstable in the nonlinear regime.

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Section: A Spherical Symmetrysupporting

confidence: 92%

Aspherical deformations of the Choptuik spacetime

Baumgarte

2018

Phys. Rev. D

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“…In addition to studying critical phenomena in the aspherical collapse of radiation fluids, this paper serves as a demonstration that an unconstrained evolution code, using "movingpuncture" coordinates, is suitable for the study of critical collapse, at least for some matter models (see also [10,23,24] for recent discussions of this issue.) We denote gridpoints with r i and define…”

Section: Discussionmentioning

confidence: 99%

“…(23)), in terms of which the focal event occurs at positive infinity. The dotted lines are fits based on (24).…”

Section: Off-center Data: Rc =mentioning

confidence: 99%

“…(8) and (9) below) have proven particularly useful for simulations of spacetimes containing black holes. How suitable these codes are for simulations of critical collapse, however, remains a somewhat open question (see also [10,23,24] for recent discussions.) Our findings here demonstrate that, at least for some matter models, unconstrained evolution codes with the 1+log and Gamma-driver coordinate conditions can indeed be used to study critical phenomena.…”

Section: Introductionmentioning

confidence: 99%

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Critical phenomena in the aspherical gravitational collapse of radiation fluids

Baumgarte

Montero

2015

Phys. Rev. D

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We study critical phenomena in the gravitational collapse of a radiation fluid. We perform numerical simulations in both spherical symmetry and axisymmetry, and observe critical scaling in both supercritical evolutions, which lead to the formation of a black hole, and subcritical evolutions, in which case the fluid disperses to infinity and leaves behind flat space. We identify the critical solution in spherically symmetric collapse, find evidence for its universality, and study the approach to this critical solution in the absence of spherical symmetry. For the cases that we consider, aspherical deviations from the spherically symmetric critical solution decay in damped oscillations in a manner that is consistent with the behavior found by Gundlach in perturbative calculations. Our simulations are performed with an unconstrained evolution code, implemented in spherical polar coordinates, and adopting "moving-puncture" coordinates.

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“…It is noticeable that there are at least two basic parameters for that, in Choptuik's original work, where the polar-areal gauge was used, the amplitude is about 0.45 [9]. In the work by Akbarian and Choptuik [36] and the work by Baumgarte [37], where the Baumgarte-Shapiro-Shibata-Nakamura formulation of Einstein's equations in spherical polar coordinates, the 1+log slicing condition for the lapse and the Gamma-driver condition for the shift were implemented, the amplitude is about 0.61. One may obtain additional hints on the nature of and possible analytic solution to critical collapse by pondering the amplitude and period together.…”

Section: The Spacetime Near the Center Is Nearly Conformally Flatmentioning

confidence: 99%

Dynamics of critical collapse

Guo

Zhang

2019

Eur. Phys. J. C

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Critical collapse of a massless scalar field in spherical symmetry is systematically studied. We combine numerical simulations and asymptotic analysis, and synthesize critical collapse, spacetime singularities, and complex science. First set of approximate analytic expressions near the center are obtained. We observe that, near the center, the spacetime is nearly conformally flat, the dynamics is not described by the Kasner solution, and the Kreschmann scalar is proportional to r −5.30 , where r is the areal radius. These features are significantly different from those in black hole singularities. It is speculated that the scalar field in critical collapse may be a special standing wave. arXiv:1808.09826v3 [gr-qc]

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Black hole critical behavior with the generalized BSSN formulation

Cited by 34 publications

References 42 publications

Aspherical deformations of the Choptuik spacetime

Aspherical deformations of the Choptuik spacetime

Critical phenomena in the aspherical gravitational collapse of radiation fluids

Dynamics of critical collapse

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