Evolution of distorted rotating black holes. I. Methods and tests

Brandt, Steven R.; Seidel, Edward

doi:10.1103/physrevd.52.856

Cited by 56 publications

(97 citation statements)

References 23 publications

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“…from the oscillations of C r = C p /C e it is possible to obtain the angular momentum of a black hole resulting from the collapse of very general configurations (see e.g. [30,31]). Finally, in Fig.…”

Section: Figmentioning

confidence: 99%

Evolving spherical boson stars on a 3D Cartesian grid

Guzmán

2004

Phys. Rev. D

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A code to evolve boson stars in 3D is presented as the starting point for the evolution of scalar field systems with arbitrary symmetries. It was possible to reproduce the known results related to perturbations discovered with 1D numerical codes in the past, which include evolution of stable and unstable equilibrium configurations. In addition, the apparent and event horizons masses of a collapsing boson star are shown for the first time. The present code is expected to be useful at evolving possible sources of gravitational waves related to scalar field objects and to handle toy models of systems perturbed with scalar fields in 3D.

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Section: Figmentioning

confidence: 99%

Evolving spherical boson stars on a 3D Cartesian grid

Guzmán

2004

Phys. Rev. D

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“…Despite the above strong advantages and although they have been widely used for 2-D (axisymmetric) computations [4][5][6][7][8][9][30][31][32], spherical coordinates are not well spread in 3-D numerical relativity. A few exceptions are the time evolution of pure gravitational wave spacetimes by Nakamura et al [30] 2 and the attempts of computing 3-D stellar core collapse by Stark [33].…”

Section: Spherical Coordinates and Numerical Techniquesmentioning

confidence: 99%

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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“…Furthermore, even with this gauge choice, if the code is run with too high a resolution, axis instabilities are again encountered, and these instabilities eventually crash the code at late times. Similar problems with axis instabilities have been encountered in the case of rotating [6,43,40,41] and colliding black holes [44,4,45,46,7,42,47].…”

Section: Rmentioning

confidence: 89%

“…Axisymmetric simulations of black holes, usually performed in spherical-polar coordinates, are typically not performed with more than 300 radial and 50 angular zones [40,41,7,42]. Inherent axis instabilities We show results for a geodesically sliced Schwarzschild black hole, evolved in 3D with the Cartoon technique.…”

Section: Rmentioning

confidence: 99%

Symmetry Without Symmetry: Numerical Simulation of Axisymmetric Systems Using Cartesian Grids

Alcubierre

Brandt

Brügmann

et al. 2001

Int. J. Mod. Phys. D

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151

188

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We present a new technique for the numerical simulation of axisymmetric systems. This technique avoids the coordinate singularities which often arise when cylindrical or polar-spherical coordinate finite difference grids are used, particularly in simulating tensor partial differential equations like those of 3 + 1 numerical relativity. For a system axisymmetric about the z axis, the basic idea is to use a 3-dimensional Cartesian (x, y, z) coordinate grid which covers (say) the y = 0 plane, but is only one finite-difference-molecule-width thick in the y direction. The field variables in the central y = 0 grid plane can be updated using normal (x, y, z)-coordinate finite differencing, while those in the y = 0 grid planes can be computed from those in the central plane by using the axisymmetry assumption and interpolation. We demonstrate the effectiveness of the approach on a set of fully nonlinear test computations in 3 + 1 numerical general relativity, involving both black holes and collapsing gravitational waves.

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Evolution of distorted rotating black holes. I. Methods and tests

Cited by 56 publications

References 23 publications

Evolving spherical boson stars on a 3D Cartesian grid

Evolving spherical boson stars on a 3D Cartesian grid

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

Symmetry Without Symmetry: Numerical Simulation of Axisymmetric Systems Using Cartesian Grids

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