Critical gravitational collapse of a perfect fluid: Nonspherical perturbations

Gundlach, Carsten

doi:10.1103/physrevd.65.084021

Cited by 32 publications

(79 citation statements)

References 14 publications

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“…Matching our numerical results to damped oscillations of the form (24) we find damping coefficients and frequencies that are within about 10% of those reported in [22]. However, our results also do not rule out the existence of a growing nonspherical mode as reported by Choptuik et.al.…”

Section: Discussionsupporting

confidence: 74%

“…We would also like to thank Carsten Gundlach for pointing us to reference [22], and for several very useful comments. TWB would like to thank the Max-Planck-Institut für Astrophysik in Garching (Germany) for its hospitality.…”

Section: Acknowledgmentsmentioning

confidence: 99%

“…Gundlach [21,22] found that perturbations of a critical solution perform damped oscillations that, up to another periodic function, can then be written in the form…”

Section: Off-center Data: Rc =mentioning

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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Section: Discussionsupporting

confidence: 74%

Section: Acknowledgmentsmentioning

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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“…Clearly, naked-singular solutions with fewer unstable modes of small eigenvalues are physically more important. Moreover, although in the above discussion we have supposed spherically symmetric perturbations, it is reasonably expected that the discussion goes similarly even for nonspherical perturbations [12]. We can also infer that the discussion also applies even to nonspherical naked-singular solutions.…”

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confidence: 94%

Border of spacetime

Harada¹,

Nakao²

2004

Phys. Rev. D

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It is still uncertain whether the cosmic censorship conjecture is true or not. To get a new insight into this issue, we propose the concept of the border of spacetime as a generalization of the spacetime singularity and discuss its visibility. The visible border, corresponding to the naked singularity, is not only relevant to mathematical completeness of general relativity but also a window into new physics in strongly curved spacetimes, which is in principle observable.PACS numbers: 04.20. Dw, 04.20.Cv In general relativity, the singularity theorems tell us that spacetime singularities exist in generic gravitational collapse spacetime (see e.g., Ref.[1]). For singularities formed in gravitational collapse, Penrose [2,3] proposed the so-called cosmic censorship conjecture, which has two versions. For spacetimes which contain physically reasonable matter fields and develop from generic nonsingular initial data, the weak one claims that there is no singularity which is visible from infinity, while the strong one claims that there is no singularity which is visible to any observer. A singularity censored by the strong version is called a naked singularity, while a singularity censored by the weak version is called a globally naked singularity. There is no general proof for the conjecture at present. Recent development on critical behavior ([4, 5], see also Ref. [6]) and self-similar attractor ([7], see also Ref. [8]) has shown that there are naked-singular solutions which result from nonsingular initial data and contain physically reasonable matter fields. The critical solution has one unstable mode while the self-similar attractor has no unstable mode against spherical perturbation, although it is still uncertain whether these examples are stable against all other possible perturbations. If all examples of naked singularities were shown to be unstable, would it mean that they are all rubbish?We have already known that general relativity will have the limitation of its applicable scale in a high-energy side. A simple and natural discussion on quantum effects of gravity yields the Planck energy E Pl ∼ 10 19 GeV as a cut-off scale Λ. Some theories with large extra dimensions may have much lower cut-off scale, which could be TeV scale [9, 10]. The energy scale of the curved spacetime can be measured by the curvature through Einstein's field equations. Then if the above expectation is true, general relativity is not applicable to the spacetime region whose curvature strength exceeds Λ 4 /E 2 Pl . This consideration naturally leads to the notion of the border of spacetime as follows. Let (M, g) be a spacetime manifold M with a metric g. We call a spacetime region A ⊂ M a border if and only if the following inequality is satisfied:where the curvature strength F is given, for instance, byWe denote the union of all borders in M by U B . We call a border A a visible border if and only ifis not empty, whereWe can also naturally define a globally visible border. To make the definition precise, we assume that the spacetime ...

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“…dipole) will determine the angular momentum of the black hole produced in slightly supercritical collapse. Using a perturbation analysis similar to that of Gundlach and Martín-García [78], Gundlach [75] (see correction in [70]) has derived the angular momentum scaling law…”

Section: Angular Momentummentioning

confidence: 99%

Critical Phenomena in Gravitational Collapse

Gundlach

2006

Encyclopedia of Mathematical Physics

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As first discovered by Choptuik, the black hole threshold in the space of initial data for general relativity shows both surprising structure and surprising simplicity. Universality, power-law scaling of the black hole mass, and scale echoing have given rise to the term "critical phenomena". They are explained by the existence of exact solutions which are attractors within the black hole threshold, that is, attractors of codimension one in phase space, and which are typically self-similar. This review gives an introduction to the phenomena, tries to summarize the essential features of what is happening, and then presents extensions and applications of this basic scenario. Critical phenomena are of interest particularly for creating surprising structure from simple equations, and for the light they throw on cosmic censorship and the generic dynamics of general relativity. * current address

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Critical gravitational collapse of a perfect fluid: Nonspherical perturbations

Cited by 32 publications

References 14 publications

Critical phenomena in the aspherical gravitational collapse of radiation fluids

Critical phenomena in the aspherical gravitational collapse of radiation fluids

Border of spacetime

Critical Phenomena in Gravitational Collapse

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