Peter Diener's WWW-exhibition

Description and visualization of particle trajectories near black holes

This WWW-exhibition will try to describe the strange kinds of motions particles can perform in the strongly relativistic regime near a black hole.

Table of contents

  1. Short introduction to general relativity
  2. Geodesics
  3. Black Holes
  4. The equations of motion
  5. The effective potential
  6. Visualization examples
  7. Examine the potential barrier
  8. Visualize your own geodesics

6. Visualization examples

In this section I will give some examples of different kinds of trajectories.

1.

Here is an example of a particle on a hyperbolic orbit in the equatorial plane of an extremally rotating black hole The parameters are the following:

      = 1.02       = 1.2       = 0.0       x = 10.0       =         -         -       = 50.0

Here is the Inventor file

Here is the VRML file

The effective potential looks like this

2.

Here is an example of a particle on a hyperbolic orbit not in the equatorial plane of an extremally rotating black hole The parameters are the following:

      = 1.01       = 1.2       = 0.8       x = 10.0       = 1.2         -         -       = 50.0

Here is the Inventor file

Here is the VRML file

The effective potential looks like this

Note that the trajectery is not constrained to a plane.

3.

Here is an example of a particle on a hyperbolic orbit that is captured by an extremally rotating black hole The parameters are the following:

      = 1.02       = -1.4       = 3.5       x = 5.0       = 1.0         -         -       = 50.0

Here is the Inventor file

Here is the VRML file

The effective potential looks like this

4.

Here is an example of a particle on a bound orbit in the equatorial plane of an extremally rotating black hole The parameters are the following:

      = 0.95       = 1.2       = 0.0       x = 5.0       =         -         -       = 1000.0

Here is the Inventor file

Here is the VRML file

The effective potential looks like this

5.

Here is an example of a particle on a bound orbit that moves slightly away from the equatorial plane of an extremally rotating black hole The parameters are the following:

      = 0.88       = 1.1       = 0.05       x = 2.0       = 1.4         -         -       = 1000.0

Here is the Inventor file

Here is the VRML file

The effective potential looks like this

6.

Here is an example of a particle on a bound orbit that moves with almost constant radial coordinate but with large variations of the polar angle. The parameters are the following:

      = 0.9501       = 0.1       = 3.2       x = 4.31       = 0.6         -         -       = 1000.0

Here is the Inventor file

Here is the VRML file

The effective potential looks like this

7.

Here is an example of a particle on an orbit starting close to the hole and returning again after having reach a maximum distance. The particle would have to be placed on this trajectory by external forces. The parameters are the following:

      = 0.965       = 0.6       = 2.2       x = 0.51       = 0.4         +         -       = 1000.0

Here is the Inventor file

Here is the VRML file

The effective potential looks like this