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Research Introduction Black Hole Critical Phenomena - Methods - Equations and Results Black Hole Accretion - Methods - Results My primary research focus is the field of numerical relativity,
specifically critical phenomena, black hole astrophysics and gravitational wave generation.
Ultimately, my goal is to simulate and understand the details of:
My doctoral dissertation research concerns the numerical study of black hole formation
from charged, massive scalar fields in spherical symmetry, and the axially symmetric accretion
of such matter onto rotating black holes and jet formation. In the gravitational collapse
to a black hole, and in accretion onto black holes, astrophysically realistic matter will
likely be magnetohydrodynamic (MHD)---fluid-like, and ionized. Only in very few
highly symmetric cases has the fully general relativistic problem (where matter sources
dynamically influence the curvature of spacetime) been completely studied. Even then,
computational techniques are required. Shock formation in fluid systems further
complicates the details. Numerical simulation of general relativistic MHD systems is in
its infancy, and insight gained through the study of MHD analogues like the charged,
massive scalar field is required for progress.
One focus of my thesis is investigating
spherically symmetric black hole formation. The threshold solution between black hole
formation and dispersal exhibits unique behavior. Originally studied for the uncharged,
massless scalar field, Choptuik found the threshold solution exhibits discrete
self-similarity (exponential rescaling in space and time reveals an identical replica)
and universality (all threshold initial data evolve to the same solution). Infinitesimal
black holes can be formed as the threshold is approached. However, while my research shows
similar results with sufficiently small charge and mass parameters, if the field is very
massive (and possibly highly charged), threshold solutions are no longer discretely
self-similar or universal. The solution in this case is different---it is now a
periodically oscillating star of charged, massive scalar material. Furthermore, there is
now a theoretical minimum mass for formed black holes. These results will be important to
the analysis of less symmetric configurations. While similar solutions have been found for
other sources, of the charged models studied, the charged, massive scalar field
most closely resembles MHD matter.
Investigation uses computational techniques---analytic
analysis can suggest details, but solving Einstein's equations of general relativity requires
numerical computation in all but the simplest of cases. I apply finite difference
methods (discrete analogue of differential methods), and use an adaptive mesh refinement
algorithm (to dynamically add resolution where necessary and remove resolution when not
required).
Equations in Postscript
Results in Postscript
In black hole accretion, astronomical evidence shows that a portion of
inspiralling plasma and generated electromagnetic radiation
collimate into bipolar jets from the black hole. Only modest
progress has been made in MHD systems, and again the details
are not well understood. In order to distinguish between matter
and gravitational effects---essential to discussion of the fully
general relativistic system---I include the axially symmetric study
of charged, massive scalar fields (i.e., the Maxwell-Klein-Gordon system)
accreting onto rotating black holes. In this case, I treat the scalar field
as test matter (it evolves about the black hole, but does not
itself contribute to the curvature of spacetime) and observe its
dynamics.
Investigation again uses the computational techniques of finite difference
methods and adaptive mesh refinement. In addition, the size of the
computational domain in axial symmetry requires the use of parallel computation
in order to obtain the results within a reasonable period of human time.
My results show that both the mass and charge coupling parameters play significant roles in structure formation and energy collimation. When the mass parameter lies with in a specific range, the scalar field persists in a region near the black hole, marking the onset of structure formation. Outside of this range, the scalar field either plunges into the back hole or mostly scatters away. But when inside this range, an additional charge coupling leads to amplification of the energy collimated along the black hole rotation axis. In addition, the dynamics display strong dynamo-like behavior in the accretion-disk plane as the axial current oscillates between the clockwise and anti-clockwise directions. This indicates how both electromagnetic and non-electromagnetic properties of the matter dramatically affect its evolution in a rotating black hole spacetime.
Last updated 02 December, 2004. Maintained by petryk@physics.ubc.ca. Supported in part by NSERC. |