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Gravitational Collapse in Axisymmetry

Gravitational Collapse in Axisymmetry. Frans Pretorius UBC http://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. Outline. Motivation

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Gravitational Collapse in Axisymmetry

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  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 variablesare 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 z=0: Initial scalar field profile and grid hierarchy (2:1 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), 2:1 refined levels (2:1 coarsened in figure) magnification factor = 1

  10. AMR grid hierarchy 17(+1), 2:1 refined levels (2:1 coarsened in figure) magnification factor ~ 17

  11. AMR grid hierarchy 17(+1), 2:1 refined levels (2:1 coarsened in figure) magnification factor ~ 130

  12. AMR grid hierarchy 17(+1), 2:1 refined levels (2:1 coarsened in figure) magnification factor ~ 330

  13. 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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