Numerical evolution of Brill waves

Garfinkle, David; Duncan, G. Comer

doi:10.1103/physrevd.63.044011

Cited by 74 publications

(244 citation statements)

References 25 publications

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“…Pretorius and Choptuik [3] performed numerical simulations of 2+1 critical gravitational collapse with a massless, minimally coupled scalar field and a cosmological constant. One of us [4] found a closed form continuously self-similar (CSS) solution of the 2+1 Einstein-scalar equations that agrees with the work of Ref. [3].…”

Section: Introductionsupporting

confidence: 70%

“…In this paper, we complete the perturbation treatment begun in [4]. Throughout we use double null coordinates rather than the Bondi coordinates used in [4]. This tends to clarify the issue of boundary conditions for the perturbations.…”

Section: Introductionmentioning

confidence: 99%

“…Thus by treating perturbations of a critical solution, one could find k and compare to the numerical value of γ found in simulations of near critical collapse. Such a perturbation treatment was begun in [4] but was not completed due to questions about appropriate boundary conditions to impose on the perturbations. In this paper, we complete the perturbation treatment begun in [4].…”

Section: Introductionmentioning

confidence: 99%

“…Such a perturbation treatment was begun in [4] but was not completed due to questions about appropriate boundary conditions to impose on the perturbations. In this paper, we complete the perturbation treatment begun in [4]. Throughout we use double null coordinates rather than the Bondi coordinates used in [4].…”

Section: Introductionmentioning

confidence: 99%

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Perturbations of an exact solution for (2+1)-dimensional critical collapse

Garfinkle¹,

Gundlach²

2002

Phys. Rev. D

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We find the perturbation spectrum of a family of spherically symmetric and continuously selfsimilar (CSS) exact solutions that appear to be relevant for the critical collapse of scalar field matter in 2+1 spacetime dimensions. The rate of exponential growth of the unstable perturbation yields the critical exponent. Our results are compared to the numerical simulations of Pretorius and Choptuik and are inconclusive: We find a CSS solution with exactly one unstable mode, which suggests that it may be the critical solution, but another CSS solution which has three unstable modes fits the numerically found critical solution better.

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Section: Introductionsupporting

confidence: 70%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Perturbations of an exact solution for (2+1)-dimensional critical collapse

Garfinkle¹,

Gundlach²

2002

Phys. Rev. D

Self Cite

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“…Furthermore, there has been a lot of work on the construction of axial codes that ensure that the metric remains smooth on the axis. For example, Garfinkle and Duncan describe in [7] a method that consists on the introduction of auxiliary variables which allow one to impose all the required regularity conditions on the extrinsic curvature. However, this method requires to solve, on every time slice, an elliptic equation for the lapse, the shift components and the conformal factor.…”

mentioning

confidence: 99%

Regularization of spherical and axisymmetric evolution codes in numerical relativity

2007

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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, cannot 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 of Rinne and Stewart and present a simple procedure to regularize the equations both in spherical and axi-symmetric spaces. We explicitly show the regularity of the evolution equations, describe the corresponding numerical code, and present several examples clearly showing the regularity of our evolutions.

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Charged star in (2+1)-dimensional gravity

Banerjee

Rahaman

Chattopadhyay

2015

Astrophys Space Sci

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We obtain a new class of exact solutions for the Einstein-Maxwell system in static spherically symmetric charged star in (2+1)-dimensional gravity. In order to obtain the analytical solutions we treat the matter distribution anisotropic in nature admitting linear or nonlinear equation of state and the electric field intensity was specified. By choosing a suitable choice of mass function m(r), it is possible to integrate the system in closed form. All the solution, which are obtained in both linear and nonlinear cases are regular at the center and well behaved in the stellar interior.Comment: 10 pages, 10 figure

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Numerical evolution of Brill waves

Cited by 74 publications

References 25 publications

Perturbations of an exact solution for (2+1)-dimensional critical collapse

Perturbations of an exact solution for (2+1)-dimensional critical collapse

Regularization of spherical and axisymmetric evolution codes in numerical relativity

Charged star in (2+1)-dimensional gravity

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