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Activities & Interests in General Relativity

Raytracing using hyperbolic light paths (1992)

Presented during the Alpbach Summer School 1992.
Unfortunately, I have no idea where I put the images from this ancient presentation...

Simulation of a Black Hole by Raytracing (1993/1994)

In this simulation it is shown what happens to a natural scene when one of these objects where a Black Hole. The bending of the light rays around a `soccerball-like' Black Hole makes normally invisible parts of the involved objects to come into view. Basic principles of gravitational lensing are demonstrated on ordinary objects and the meaning of the Einstein ring is explained also.

Published in:

Voids (Diplomarbeit, 1997)

Der Einfluß der kosmologischen Konstanten auf die Vakuumblasen im expandierenden Universum

Voids (Diploma thesis, 1997)

The Influence of the Cosmological Constant on the Voids in the Expanding Universe (german only)

The Tolman dust metric with cosmological constant was used to model a spherically symmetric inhomogenious universe. Small density perturbations at the beginning of the matter dominated phase are traced during their evolution within the expansion of the universe and their final properties are compared in the standard model (using an Hubble constant of 50km/s/Mpc, zero cosmological constant and critical density) to the world model by Wolfgang Priester

An interactive interface for computing the Friedmann-Lemaitre universe and the inhomogenius dust cosmos is also available here.

The Black Earth (1997)

or: The Day, when Earth became a Black Hole

For an intuitive insight into the curvature of space due to the gravitational field, it is suitable and impressive to see the effects of curved space act on well known objects. This simulation series was made to demonstrate the visual effect that would occur if Earth became a Black Hole from one day to another. Special attention was given to demonstrate the properties of the Photon Orbit, where light rays may orbit the central on an perfect circle.

ART - a project for the interactive visualization and exploration of numerically found curved spacetimes (1997-2005)

80 years after invention of the Theory of General Relativity (German: "Allgemeine Relativitätstheorie" - ART) many questions remain unsolved, among them the generic solution of the presumably simple two-body problem. Only numerical methods are applicable. Various research groups around the world are working on these ``grand challenge'' problems, which requires solving Einstein's equation for the gravitational field in the full generic case. Only then it will be possible to study astrophysically relevant situations.

Numerical solutions cannot be investigated on just `a sheet of paper' like analytical solutions. These modern solution methods thus require three and four-dimensional visualization techniques.

This is the goal of the ART project, a collaboration project between ZIB and AEI.

New Frontiers in Relativistic Visualization (2005-2008)

At Louisiana State University

More to come here...


Articles and images from these projects appeared in many journals and books.
The first grazing collision of two black holes was performed in June 1999 at NCSA. This dataset showed very clear structures and its visualizations were spreading around soon. The central part displays the color-coded horizons. The original version used white/yellow/red colors for depicting high/medium/low intensity of the gravitational radiation around. Some years later, I made a more dynamically looking version for the magazine GEO which used a colormap with shades ranging from red via yellow to green and blue. This image and its variants is now used in many places.

The efforts of this 1999 visualization marathon are described in SuW Special 6 Gravitation (German).

Beobachtungen im Datenraum
SuW Special 6 Gravitation

Gravity from the Ground Up
Bernard Schutz

The Future of Theoretical Physics an Cosmology
Celebrating Stephen Hawking's 60th Birthday
Jagd auf Gravitationswellen
Spektrum der Wissenschaften - Jagd auf Gravitationswellen
December 2000 Issue

Access Magazine 1999

Max Planck Research
MPG 1999

Naturwissenschaftliche Rundschau 11/2005

LIGO Folder

Communications of the ACM
Vol. 46, No. 11, Nov 2001

Science & Vie
No. 1011, Nov 2002

IEEE Computer
Dec. 1999
Timelike Geodesics in the Kerr Spacetime. Trajectories of test particles in the vicinity of rotating black hole yield aesthetically pleasing regular pattern. The computation is based on the CACTUS thorn TimeGeodesics, developed by Miguel Alcubierre. It has been equipped with an network interface to allow remote visualization.

The visual results are appealing to scientists as well as to artists.

Visualization and Processing of Tensor Fields
Joachim Weickert, Hans Hagen; Springer Verlag
C - The Speed Of Light
Einstein Opera by Phase 7
Nancy Walker

Das Einstein-Fenster
Markus Poessl

Der Stern von Bethlehem in astronomischer Sicht
Konradin Ferrari d'Occhieppo
More activities:
- Blind Date - Art meets Science; an art exhibition initiated by the Brandenburgischer Kunstverein, on the topic "Event Horizon", together with artist Susanne Weirich
- TV Interview in german financial magazine "Frontal21", 12. November 2002, Eichels schwarze Löcher
The GRG18 announcement poster contains lots of my images.

Further Recommendations:

- University of Tuebingen - Films & Movies on Special and General Relativity - Special Relativity and General Relativity Raytracing

- Ray Tracing with Curved Light Beams (done by Per Christian Ødegård) - greatly, this page has appeared again after it was hidden for a long time and Christian's mail was accidentally moved automatically into my SPAM folder, but his thesis was such excellent that I kept this link here to remind myself and the rest of the world of this page.

- Virtual Trips to Black Holes and Neutron Stars

- Too close to a Black Hole (Astronomy Picture of the Day November 27, 1995), or via Black Hole Index

- Black Hole Simulations (Sam Hart, Arizona)

- Falling into a Black Hole (Andrew Hamilton, Colorado)

- Null Geodesics Around a Kerr Black Hole (Bo Milvang-Jensen, Denmark)

- Yahoo Black Hole Directory

- Andrew Howard - relativistic raytracing

- Seeing Relativity The Backlight Raytracer at the Austrial National University - best special relativistic rendering seen so far!

- Relativistic raytracing of lattices

- The Light Cone (by Rob Salgado)

- Web Course on Gravitational Waves (by Kip Thorne, Mihai Bondarescu and Yanbei Chen)

- Excellent Cosmology FAQ (by Ned Wright)

- CarpetCode - Numerical Simulations of General Relativity