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

8. Visualize your own geodesics

Here you have the chance to specify orbital parameters for particle motions in the vicinity of a black hole. You can do this in two different ways. Here you can specify the initial position and velocity for a massive particle. Here you can specify the initial position along with the constants of motion (energy, angular momentum around the z-axis and Carter's fourth constant) for a massive particle.

Orbital parameters for massive particles

Black hole parameters

Enter black hole rotation parameter ( )  

Particle parameters

Specify the initial position of the particle. The coordinate and time coordinate are irrelevant because of symmetry and are arbitrarily assigned the values 0.0.

x          

Specifiy the initial 4-velocity of the particle. The time component is not independent, but is given by the condition that the norm of the 4 velocity is -1.

                 

Time parameters

Specify the interval of proper time to be covered

 

Orbital parameters for massive particles

Black hole parameters

Enter black hole rotation parameter ( )  

Particle parameters

Specify the constants of motion.

                 

Specify the initial position of the particle. The phi coordinate and time coordinate are irrelevant because of symmetry and are arbitrarily assigned the values 0.0. The radial coordinate is not necessary in order to fix the orbit, but is used to select a starting point for the orbit.

NB. Note that not all values of the radial coordinate and polar angle are consistent with the values of the constants of motion. If an inconsistent value of radial coordinate is chosen use the plot of the effective potential to find a better value. If an inconsistent value of the polar angle is chosen, the program will use instead.

x          

Specify the sign of and .

    -     +               -     +

Time parameters

Specify the interval of proper time to be covered