# Visualisation in special and general relativity

## Introduction

Einstein's theories of special and general relativity describe space and time not as two separate, absolute entities, but they combine space and time to one single entity – the so called spacetime. Special relativity concentrates on relative motion between reference frames close to the speed of light in flat Minkowskian spacetime. General relativity describes gravity as a geometric property of spacetime itself.

The effects of both theories are far from our daily experiences. Even with the most modern propulsion systems, we move with velocities far below the speed of light; and the mass of Earth curves spacetime only such that we stay on the ground. The effects of general relativity become apparent only if big masses are concentrated in small regions. The most extreme example is a black hole, where the curvature of spacetime is so strong that even light cannot escape.

While Special relativity is quite simple in mathematically and can be discussed on high school level, general relativity is quite demanding. In particular, a freshman has difficulties with the mathematics of general relativity and also its physical implications.

Here, computer simulations help by providing visual access to both theories. Phenomena like aberration of light, length contraction or bending of light can be experienced. Hence, we obtain an intuitive access to special and general relativity.

 Observer is moving with 90 % the speed of light. View through a Morris-Thorne wormhole.

## Visualisation techniques

The most natural technique for relativistic visualisation is ray tracing. Particularly, the finiteness of the speed of light has to be taken into account when extending the ray tracing methog from three to four dimensions. Additionally, we have to consider the frequency-shift caused by the Doppler effect and gravitational fields, bending of light due to the curved spacetime as well as light amplification. Four-dimensional relativistic ray tracing delivers high-quality images, however, it is very time consuming and thus, in general, not suitable for interactive visualisation.

For special relativity, image-based methods and polygon rendering are two techniques that make interactive visualisation feasible. Both methods make use of modern graphics hardware for either an image-space or an object-space transformation. However, there are limitations concerning the scene and the motion of objects with both techniques. A recently developed third method combines polygon rendering with local ray tracing and thus circumvents the shortcomings of the underlying methods.

For general relativity, interactive visualisations are possible only by means of analytic solutions of the equations of motion for light or particles. In case of a highly symmetric spacetime geometry, simple scenaries can be visualised with interactive frame rates by means of precalculations and tabulating.

## Projects

### Visualization of light- and timelike geodesics in multi black hole spacetimes in the general theory of relativity

A detailled description can be found here. (Coming soon)

### Interactive visualization of a thin disk around a Schwarzschild black hole

A detailed description can be found here.

### GPU-based four-dimensional general-relativistic ray tracing

A detailed description can be found here.

### Detailed study of null and time-like geodesics in the Alcubierre Warp spacetime.

A detailed description can be found here.

### Studying null and time-like geodesics in the classroom.

A detailed description can be found here.

### GeodesicViewer - A tool for exploring geodesics in the theory of relativity

A detailed description can be found here.

### Visualizing circular motion around a Schwarzschild black hole

A detailed description can be found here.

### Distortion of the stellar sky by a Schwarzschild black hole

A detailed description can be found here.

### A trip to the end of the universe and the twin "paradox"

A detailed description can be found here.

### Visualization of the General Relativistic Disk of Dust

A detailed description can be found here.

### A Case Study on Explanatory and Illustrative Visualization of Relativity and Astrophysics

A detailed description can be found here.

### Minkowski Diagrams

A detailed description of the Java2 application can be found here.

### Relativistic Movement Viewer

A detailed description can be found here.

## Gallery

SR gallery

GR gallery

### Publications

1. Müller, Thomas ; Fechtig, Oliver: Empirical exploration of timelike geodesics around a rotating wormhole. In: of Physics, A. J. (Hrsg.) American Journal of Physics, American Journal of Physics. Bd. 84 (2016), Nr. 5, S. 375–383
2. Müller, Thomas: Image-based general-relativistic visualization. In: of Physics, E. J. (Hrsg.) Bd. 36 (2015)
3. Müller, Thomas ; Boblest, Sebastian ; Weiskopf, Daniel: Visualization Showcase: General-Relativistic Black Hole Visualization. In: Association, T. E. ; Association, T. E. (Hrsg.) ; Association, T. E. (Hrsg.): Eurographics Symposium on Parallel Graphics and Visualization, Eurographics Symposium on Parallel Graphics and Visualization, 2015
4. Müller, Thomas ; Boblest, Sebastian: Visual appearance of wireframe objects in special relativity. In: European Journal of Physics, European Journal of Physics. Bd. 35 (2014)
5. Müller, Thomas: GeoViS – Relativistic ray tracing in four-dimensional spacetimes. In: Computer Physics Communications, Computer Physics Communications. Bd. 185 (2014)
6. Frutos-Alfaro, Francisco ; Grave, Frank ; Müller, Thomas ; Adis, Daria: Wavefronts and Light Cones for Kerr Spacetimes. In: Journal of Modern Physics, Journal of Modern Physics. Bd. 3 (2012)
7. Müller, Thomas ; Frauendiener, Jörg: Interactive visualization of a thin disc around a Schwarzschild black hole. In: European Journal of Physics, European Journal of Physics. Bd. 33 (2012)
8. Kuchelmeister, Daniel ; Müller, Thomas ; Ament, Marco ; Wunner, Günter ; Weiskopf, Daniel: GPU-based four-dimensional general-relativistic ray tracing. In: Computer Physics Communications, Computer Physics Communications. Bd. 183 (2012)
9. Müller, Thomas ; Weiskopf, Daniel: Detailed study of null and timelike geodesics in the Alcubierre warp spacetime. In: General Relativity and Gravitation, General Relativity and Gravitation. Bd. 44 (2012)
10. Müller, Thomas ; Weiskopf, Daniel: General-Relativistic Visualization. In: Computing in Science & Engineering, Computing in Science & Engineering. Bd. 13 (2011a), Nr. 6
11. Müller, Thomas ; Weiskopf, Daniel: Special-Relativistic Visualization. In: Computing in Science & Engineering, Computing in Science & Engineering. Bd. 13 (2011b), Nr. 4
12. Boblest, Sebastian ; Müller, Thomas ; Wunner, Günter: Twin paradox in de Sitter spacetime. In: European Journal of Physics, European Journal of Physics. Bd. 32 (2011)
13. Müller, Thomas ; Frauendiener, Jörg: Studying null- and time-like geodesics in the classroom. In: European Journal of Physics, European Journal of Physics. Bd. 32 (2011)
14. Müller, Thomas: Analytic observation of a star orbiting a Schwarzschild black hole. In: Gen. Rel. Grav., Gen. Rel. Grav. Bd. 41 (2008a)
15. Müller, Thomas: Einstein rings as a tool for estimating distances and the mass of a Schwarzschild black hole. In: Phys. Rev. D, Phys. Rev. D. Bd. 77 (2008b)
16. Müller, Thomas: Falling into a Schwarzschild black hole - Geometric aspects. In: Gen. Rel. Grav., Gen. Rel. Grav. (2008d)
17. Grave, Frank ; Buser, Michael ; Müller, Thomas ; Wunner, Günter ; Schleich, Wolfgang P.: The Gödel universe: Exact geometrical optics and analytical investigations on motion. In: Physical Review D, Physical Review D. Bd. 80 (2009a)
18. Müller, Thomas ; Grave, Frank: Motion4D - A library for lightrays and timelike worldlines in the theory of relativity. In: Computer Physics Communications, Computer Physics Communications. Bd. 180 (2009)
19. Grave, Frank ; Müller, Thomas ; Dachsbacher, Carsten ; Wunner, Günter: The Gödel Engine - An interactive approach to visualization in general relativity. In: Computer Graphics Forum, Computer Graphics Forum. Bd. 28 (2009b), Nr. 3
20. Müller, Thomas ; Grave, Frank: GeodesicViewer - A tool for exploring geodesics in the theory of relativity. In: Computer Physics Communications, Computer Physics Communications. Bd. 181 (2010)
21. Müller, Thomas ; Boblest, Sebastian: Visualizing circular motion around a Schwarzschild black hole. In: American Journal of Physics, American Journal of Physics. Bd. 79 (2011)
22. Ruder, Hanns ; Weiskopf, Daniel ; Nollert, Hans-Peter ; Müller, Thomas: How Computers Can Help Us in Creating an Intuitive Access to Relativity. In: New Journal of Physics, New Journal of Physics. Bd. 10 (2008)
23. Müller, Thomas ; Grottel, Sebastian ; Weiskopf, Daniel: Special Relativistic Visualization by Local Ray Tracing. In: IEEE Transactions on Visualization and Computer Graphics, IEEE Transactions on Visualization and Computer Graphics. Bd. 16 (2010), Nr. 6
24. Müller, Thomas ; Weiskopf, Daniel: Distortion of the stellar sky by a Schwarzschild black hole. In: American Journal of Physics, American Journal of Physics. Bd. 78 (2010), Nr. 2
25. Müller, Thomas ; King, Andreas ; Adis, Daria: A trip to the end of the universe and the twin paradox. In: Am. J. Phys, Am. J. Phys. (2008)
26. Müller, Thomas: Exact geometric optics in a Morris-Thorne wormhole spacetime. In: Phys. Rev. D, Phys. Rev. D. (2008c)
27. Ruder, Hanns ; Weiskopf, Daniel: Simulation und Visualisierung in der Astrophysik oder die wundersame Reise des Christoph Zenger mit der U.S.S. Enterprise. In: Bungartz, H. J. ; Zimmer, S. ; Bungartz, H. J. ; Zimmer, S. (Hrsg.) ; Bungartz, H. J. ; Zimmer, S. (Hrsg.): Numerische Simulation als interdisziplinäre Herausforderung: Beiträge zum 60. Geburtstag von C. Zenger, Numerische Simulation als interdisziplinäre Herausforderung: Beiträge zum 60. Geburtstag von C. Zenger : Springer, 2002
28. Kobras, D. ; Weiskopf, Daniel ; Ruder, Hanns: General relativistic image-based rendering. In: The Visual Computer, The Visual Computer. Bd. 18 (2002), Nr. 4
29. Kraus, Ute ; Ruder, Hanns ; Weiskopf, Daniel ; Zahn, C.: Was Einstein noch nicht sehen konnte. Schnelle Computer visualisieren relativistische Effekte. In: Physik Journal, Physik Journal. (2002), Nr. 7
30. Kobras, D. ; Weiskopf, Daniel ; Ruder, Hanns: Image-Based Rendering and General Relativity. In: Proceedings of WSCG’01, Proceedings of WSCG’01, 2001