Max-Planck-Institut
für Gravitationsphysik
Albert-Einstein-Institut
Konrad-Zuse-Zentrum für
Informationstechnik Berlin (ZIB)
Scientific Visualization


Geodesics in Kerr Space-Time

Particle trajectories in the curved space-time of a rotating black hole

Space-time is a physical concept of the four dimensional continuum we live in. According to our current knowledge it is best described by Einstein's theory of general relativity. 'Geodesics' are the shortest lines between two points. In general relativity, the path of a freely falling particle is a `timelike geodesic'. It is determined by the geometry of space-time and the initial velocity of the particle only. The principle of equivalence, one of the fundaments of Reneral relativity, states that this particle trajectory does not depend on the mass of the particle.

In our general relativity research projects the Cactus computer code is used to numerically evolve space-times, which cannot be treated by analytic means, e.g. the collision of black holes or neutron stars. Such simulations require immense computational resources and - for large-scale simulations - run on supercomputers. In such a numerical space-time we may place `seeds' of particles, being at rest initially. These particles will then be influenced by the simulated gravitational field.

While CACTUS runs on a supercomputer located in a high-performance computing center somewhere in the world, the particle positions are sent to a local graphics workstations running Amira for visualization. The `Illuminated Stream Line' technique, special to Amira (developed at ZIB), is used to display the path of the virtual particles as they are dragged around in the numerically evolved space-time.

The examples presented here show particles in the Kerr space-time. This is the analytically known solution of a rotating black hole. However, while the space-time is known in this demonstration example, the particle's world lines cannot be determined analytically and have to be computed numerically.

Note that the influence of the rotation of the black hole on the particle paths is a non-newtonian effect. This effect, also called the `gravitomagnetism', is one of the yet unverified expectations of Einstein's theory of general relativity.


Snapshots from a real time visualization done with Amira and the simulation system Cactus

More images available here.


Contributions and References

Last update: July 3, 2000 G. Skorobohatyj ZIB Homepage