next up previous contents
Next: Visualization results part two Up: Interactivity Previous: CGI scripts

Do it yourself null geodesic

By using the interactive form below, you can create a 3D scene with your own null geodesics. This is a very good way of getting a feeling of how light rays move around a rotating black hole.

Black hole properties

M   =     (mass)
a/M   =     (measure of rotation, 0 \leq a/M \leq 1 )

Initial position of photon

r   =     (you must have r gt r_H=M+(M^2-a^2)^1/2 )
theta   =     [radians]
phi   =     [radians] (unimportant, since there is symmetry around the z-axis)
t   =     (unimportant, since the metric is time independent)

Note: You can specify pi (pi) as   !pi   in the normal IDL fasion.

Initial direction of photon

dr   =  
dtheta   =     [radians]
dphi   =     [radians]
Note: Here, a null geodesic is obtained by solving ds^2=0 for dt. Therefore, the user cannot specify dt.

Affine parameter control

dlambda   =     (affine parameter step size)
# steps   =     (max 10,000)

3D scene format


Note: you have to manually switch on "Headlight" (in the "View" menu) in WebSpace to be able to see the 3D widgets below. In ivview there seems to be light everywhere.

Drawing style of geodesic


Note: I think that Line looks the best, but Points allows you too see (more clearly) the spacing between the points. Try sending the photon directly towards a nonrotating black hole, e.g. a/M=0, dr=-0.5, dtheta=0, and dphi=0.

Color of geodesic

R   =     G   =     B   =  

Coordinate system widget

  • Enabled   or   Disabled
  • Axis length   =  
  • Label x axis with 3D letter "x": yes   or   no

Note: the x, y, and z axis are red, green, and blue, respectively, and have a transparency of 0.25. If you cannot view color, you should enable the x axis labeling, and then find the y and z axis using the right hand rule.

Horizon widget

  • Enabled   or   Disabled
  • Radius: r   =   r_H=M+(M^2-a^2)^1/2   or   r   =  
  • Color:   R   =     G   =     B   =  
  • Transparency   =  
Note: you can of course get a black horizon instead of a yellow one by setting R=G=B=0 !

Static Limit / Ergosphere widget

  • Enabled   or   Disabled
  • Color:   R   =     G   =     B   =  
Note: the static limit is given by  .
It is shown as a wire mesh.


(be patient!) or
Note: when your browser says "Connect: Host contacted. Waiting for reply...", my machine is actually calculating the null geodesic you specified.
Typical calculation time: 10 seconds.

Web Exhibition: Null Geodesics Around a Kerr Black Hole

Bo Milvang-Jensen (
Mon Jun 17 11:54:08 MDT 1996