Gravitational Collapse in Axisymmetry

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Gravitational Collapse in Axisymmetry
Frans Pretorius UBChttp//laplace.physics.ubc.ca
/People/fransp/
APS Meeting Albuquerque, New Mexico April 20,
2002

• Collaborators
• Matthew Choptuik, CIAR/UBC
• Eric Hircshmann, BYU
• Steve Liebling, LIU

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Outline

• Motivation
• Overview of the physical system
• Adaptive Mesh Refinement (AMR) in our numerical
  code
• Critical phenomena in axisymmetry
• Conclusion near future extensions

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Motivation

• Our immediate goal is to study critical behavior
  in axisymmetry
• massless, real scalar field
• Brill waves
• introduce angular momentum via a complex scalar
  field
• Long term goals are to explore a wide range
  axisymmetric phenomena
• head-on black hole collisions
• black hole - matter interactions
• incorporate a variety of matter models, including
  fluids and electromagnetism

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Physical System

• Geometry
• Matter a minimally-coupled, massless scalar
  field
• All variables are functions of
• Kinematical variables
• Dynamical variables

and are the conjugates to and
,respectively
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Adaptive Mesh Refinement

• Our technique is based upon the Berger Oliger
  algorithm
• Replace the single mesh with a hierarchy of
  meshes
• Recursive time stepping algorithm
• Efficient use of resources in both space and time
• Geared to the solution of hyperbolic-type
  equations
• Use a combination of extrapolation and delayed
  solution for elliptic equations
• Dynamical regridding via local truncation error
  estimates (calculated using a self-shadow
  hierarchy)
• Clustering algorithms
• The signature-line method of Berger and Rigoutsos
  (using a routine written by R. Guenther, M. Huq
  and D. Choi)
• Smallest, non-overlapping rectangular bounding
  boxes

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2D Critical Collapse example

• Initial data that is anti-symmetric about z0

Initial scalar field profile and grid hierarchy
(21 coarsened in figure)
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Anti-symmetric SF collapse
Scalar field Weak field evolution
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Anti-symmetric SF collapse
Scalar field Near critical evolution
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AMR grid hierarchy
17(1), 21 refined levels (21 coarsened in
figure)
magnification factor 1
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AMR grid hierarchy
17(1), 21 refined levels (21 coarsened in
figure)
magnification factor 17
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AMR grid hierarchy
17(1), 21 refined levels (21 coarsened in
figure)
magnification factor 130
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AMR grid hierarchy
17(1), 21 refined levels (21 coarsened in
figure)
magnification factor 330
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Conclusion

• Near future work
• More thorough study of scalar field critical
  parameter space
• Improve the robustness of the multigrid solver,
  to study Brill wave critical phenomena
• Include the effects of angular momentum
• Incorporate excision into the AMR code
• Add additional matter sources, including a
  complex scalar field and the electromagnetic
  field