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Gravitational Collapse in Axisymmetry

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... error estimates (calculated using a self-shadow hierarchy) ... Smallest, non-overlapping rectangular bounding boxes. 6. 2D Critical Collapse example ... – PowerPoint PPT presentation

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Title: Gravitational Collapse in Axisymmetry


1
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

2
Outline
  • Motivation
  • Overview of the physical system
  • Adaptive Mesh Refinement (AMR) in our numerical
    code
  • Critical phenomena in axisymmetry
  • Conclusion near future extensions

3
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

4
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
5
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

6
2D Critical Collapse example
  • Initial data that is anti-symmetric about z0

Initial scalar field profile and grid hierarchy
(21 coarsened in figure)
7
Anti-symmetric SF collapse
Scalar field Weak field evolution
8
Anti-symmetric SF collapse
Scalar field Near critical evolution
9
AMR grid hierarchy
17(1), 21 refined levels (21 coarsened in
figure)
magnification factor 1
10
AMR grid hierarchy
17(1), 21 refined levels (21 coarsened in
figure)
magnification factor 17
11
AMR grid hierarchy
17(1), 21 refined levels (21 coarsened in
figure)
magnification factor 130
12
AMR grid hierarchy
17(1), 21 refined levels (21 coarsened in
figure)
magnification factor 330
13
(No Transcript)
14
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
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