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Kerr wave-fronts results

The results presented here are the work of Charles Harnden, Scott Johnson, John Rossman, Rob Schweitzer and Scott Schlef (as part of fall 2008 Physics 422: Computational Methods in the Physical Sciences) at Bridgewater State College.  Scott Johnson and John Rossman continued working on this project during the spring 2009 semester.  This work was supported in part by an Adrian Tinsley Program Course Grant and a BSC Presidential Course Development Grant.  The work was motivated by a research workshop of the American Institute of Mathematics on Gravitational Lensing in the Kerr Space-time Geometry.   

To left:

Three wave-fronts advancing from right to left
passing the even horizon of a Kerr black hole
with a = 0.25 and m=1.  The wave-fronts are those
emitted from a point source at r = 20 in the
equitorial plane.  The circular blank region in the
wave-front is omitted data that falls into the black
hole.

These wave-fronts are constant t wave-fronts in
usual Boyer-Lindquist coordinates.

To right:

Same wave-front progressions as above at later times.

 

Wave-front data was generated using an adaptive
stepsize Runge-Kutta-Fehlberg 4-5 methods based
loosely on the presentation in NR of Press et al.

We integrate the individual light rays emanating from
a point and place data into level t wave-front files.  The
wave-fronts are then produced graphically using the ListPointPlot3D command from Mathematica 7. 

Thomas Kling, Arlie Petters (Duke University) and BSC Students Scott Johnson and John Rossman discussing Kerr wave-fronts at Duke in February 2009.

 

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