An axisymmetric gravitational collapse code

Choptuik, Matthew W.; Hirschmann, Eric; Liebling, Steven L.; Pretorius, Frans

doi:10.1088/0264-9381/20/9/318

Cited by 72 publications

(167 citation statements)

References 28 publications

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“…Still in the 2-D axisymmetric case, fully constrained schemes have been used by Evans [7] and Shapiro and Teukolsky [8] for non-rotating spacetimes, and by Abrahams, Cook, Shapiro and Teukolsky [9] for rotating ones. We also notice that the recent (2+1)+1 axisymmetric code of Choptuik et al [10] is based on a constrained scheme too.…”

Section: A Motivations For a Constrained Schemementioning

confidence: 82%

Constrained scheme for the Einstein equations based on the Dirac gauge and spherical coordinates

et al. 2004

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We propose a new formulation for 3+1 numerical relativity, based on a constrained scheme and a generalization of Dirac gauge to spherical coordinates. This is made possible thanks to the introduction of a flat 3-metric on the spatial hypersurfaces t = const, which corresponds to the asymptotic structure of the physical 3-metric induced by the spacetime metric. Thanks to the joint use of Dirac gauge, maximal slicing and spherical components of tensor fields, the ten Einstein equations are reduced to a system of five quasi-linear elliptic equations (including the Hamiltonian and momentum constraints) coupled to two quasi-linear scalar wave equations. The remaining three degrees of freedom are fixed by the Dirac gauge. Indeed this gauge allows a direct computation of the spherical components of the conformal metric from the two scalar potentials which obey the wave equations. We present some numerical evolution of 3-D gravitational wave spacetimes which demonstrates the stability of the proposed scheme.

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Section: A Motivations For a Constrained Schemementioning

confidence: 82%

Constrained scheme for the Einstein equations based on the Dirac gauge and spherical coordinates

et al. 2004

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“…As a first step, we wish to develop adaptive mesh refinement procedures for conserva-tive systems that will be required to study critical phenomena of stellar objects in axial-symmetry [54].…”

Section: Discussionmentioning

confidence: 99%

Type II critical phenomena of neutron star collapse

Noble

Choptuik

2008

Phys. Rev. D

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We investigate spherically-symmetric, general relativistic systems of collapsing perfect fluid distributions. We consider neutron star models that are driven to collapse by the addition of an initially "in-going" velocity profile to the nominally static star solution. The neutron star models we use are Tolman-Oppenheimer-Volkoff solutions with an initially isentropic, gamma-law equation of state.The initial values of 1) the amplitude of the velocity profile, and 2) the central density of the star, span a parameter space, and we focus only on that region that gives rise to Type II critical behavior, wherein black holes of arbitrarily small mass can be formed. In contrast to previously published work, we find that-for a specific value of the adiabatic index (Γ = 2)-the observed Type II critical solution has approximately the same scaling exponent as that calculated for an ultrarelativistic fluid of the same index. Further, we find that the critical solution computed using the ideal-gas equations of state asymptotes to the ultrarelativistic critical solution.

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“…This is a very ideal case and there have been many attempts to study the problem with less symmetry, for example, in the spacetimes with axial symmetry [6], in which only one spacelike Killing vector exists. However, analytical studies of these spacetimes seem still far beyond our reach.…”

Section: Introductionmentioning

confidence: 99%