Frank Grave

Explanatory and illustrative visualization of special and general relativity

This paper describes methods for explanatory and illustrative visualizations used to communicate aspects of Einsteins theories of special and general relativity, their geometric structure, and of the related fields of cosmology and astrophysics. Our illustrations target a general audience of laypersons interested in relativity. We discuss visualization strategies, motivated by physics education and the didactics of mathematics, and describe what kind of visualization methods have proven to be useful for different types of media, such as still images in popular science magazines, film contributions to TV shows, oral presentations, or interactive museum installations. Our primary approach is to adopt an egocentric point of view: the recipients of a visualization participate in a visually enriched thought experiment that allows them to experience or explore a relativistic scenario. In addition, we often combine egocentric visualizations with more abstract illustrations based on an outside view in order to provide several presentations of the same phenomenon. Although our visualization tools often build upon existing methods and implementations, the underlying techniques have been improved by several novel technical contributions like image-based special relativistic rendering on GPUs, special relativistic 4D ray tracing for accelerating scene objects, an extension of general relativistic ray tracing to manifolds described by multiple charts, GPU-based interactive visualization of gravitational light deflection, as well as planetary terrain rendering. The usefulness and effectiveness of our visualizations are demonstrated by reporting on experiences with, and feedback from, recipients of visualizations and collaborators.

GeodesicViewer – A tool for exploring geodesics in the theory of relativity ☆

Abstract The GeodesicViewer realizes exocentric two- and three-dimensional illustrations of lightlike and timelike geodesics in the general theory of relativity. By means of an intuitive graphical user interface, all parameters of a spacetime as well as the initial conditions of the geodesics can be modified interactively. New version program summary Program title: GeodesicViewer Catalogue identifier: AEFP_v2_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEFP_v2_0.html Program obtainable from: CPC Program Library, Queenʼs University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 76 202 No. of bytes in distributed program, including test data, etc.: 1 722 290 Distribution format: tar.gz Programming language: C++, OpenGL Computer: All platforms with a C++ compiler, Qt, OpenGL Operating system: Linux, Mac OS X, Windows RAM: 24 MBytes Classification: 1.5 External routines: • Motion4D (included in the package) • Gnu Scientific Library (GSL) ( http://www.gnu.org/software/gsl/ ) • Qt ( http://qt.nokia.com/downloads ) • OpenGL ( http://www.opengl.org/ ) Catalogue identifier of previous version: AEFP_v1_0 Journal reference of previous version: Comput. Phys. Comm. 181 (2010) 413 Does the new version supersede the previous version?: Yes Nature of problem: Illustrate geodesics in four-dimensional Lorentzian spacetimes. Solution method: Integration of ordinary differential equations. 3D-Rendering via OpenGL. Reasons for new version: The main reason for the new version was to visualize the parallel transport of the Sachs legs and to show the influence of curved spacetime on a bundle of light rays as is realized in the new version of the Motion4D library ( http://cpc.cs.qub.ac.uk/summaries/AEEX_v3_0.html ). Summary of revisions: • By choosing the new geodesic type “lightlike_sachs”, the parallel transport of the Sachs basis and the integration of the Jacobi equation can be visualized. • The 2D representation via Qwt was replaced by an OpenGL 2D implementation to speed up the visualization. • Viewing parameters can now be stored in a configuration file (.cfg). • Several new objects can be used in 3D and 2D representation. • Several predefined local tetrads can be choosen. • There are some minor modifications: new mouse control (rotate on sphere); line smoothing; current last point in coordinates is shown; mutual-coordinate representation extended; current cursor position in 2D; colors for 2D view. Running time: Interactive. The examples given take milliseconds.

Motion4D – A library for lightrays and timelike worldlines in the theory of relativity☆

Abstract The Motion4D-library solves the geodesic equation as well as the parallel- and Fermi–Walker-transport in four-dimensional Lorentzian spacetimes numerically. Initial conditions are given with respect to natural local tetrads which are adapted to the symmetries or the coordinates of the spacetime. Beside some already implemented metrics like the Schwarzschild and Kerr metric, the object oriented structure of the library permits to implement other metrics or integrators in a straight forward manner. Program summary Program title: Motion4D-library Catalogue identifier: AEEX_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEEX_v1_0.html Program obtainable from: CPC Program Library, Queens University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 150 425 No. of bytes in distributed program, including test data, etc.: 5 139 407 Distribution format: tar.gz Programming language: C++ Computer: All platforms with a C++ compiler Operating system: Linux, Unix, Windows RAM: 39 MBytes Classification: 1.5 External routines: Gnu Scientific Library (GSL) ( http://www.gnu.org/software/gsl/ ) Nature of problem: Solve geodesic equation, parallel and Fermi–Walker transport in four-dimensional Lorentzian spacetimes. Solution method: Integration of ordinary differential equations Running time: The test runs provided with the distribution require only a few seconds to run.

Visualization in the Einstein Year 2005: a case study on explanatory and illustrative visualization of relativity and astrophysics

In this application paper, we report on over fifteen years of experience with relativistic and astrophysical visualization, which has been culminating in a substantial engagement for visualization in the Einstein Year 2005 - the 100/sup th/ anniversary of Einsteins publications on special relativity, the photoelectric effect, and Brownian motion. This paper focuses on explanatory and illustrative visualizations used to communicate aspects of the difficult theories of special and general relativity, their geometric structure, and of the related fields of cosmology and astrophysics. We discuss visualization strategies, motivated by physics education and didactics of mathematics, and describe what kind of visualization methods have proven to be useful for different types of media, such as still images in popular-science magazines, film contributions to TV shows, oral presentations, or interactive museum installations. Although our visualization tools build upon existing methods and implementations, these techniques have been improved by several novel technical contributions like image-based special relativistic rendering on GPUs, an extension of general relativistic ray tracing to manifolds described by multiple charts, GPU-based interactive visualization of gravitational light deflection, as well as planetary terrain rendering. The usefulness and effectiveness of our visualizations are demonstrated by reporting on experiences with, and feedback from, recipients of visualizations and collaborators.

The gödel engine - an interactive approach to visualization in general relativity

We present a methodical new approach to visualize the aspects of general relativity from a self‐centered perspective. We focus on the visualization of the Gödel universe, which is an exact solution to Einsteins field equations of general relativity. This model provides astounding features such as the existence of an optical horizon and the possibility of time travel. Although we know that our universe is not of Gödel type, we can – using this solution to Einsteins equations – visualize and understand the effects resulting from the theory of relativity, which itself has been verified on the large scale in numerous experiments over the last century. We derive the analytical solution to the geodesic equations of Gödels universe for special initial conditions. Along with programmable graphics hardware we achieve a tremendous speedup for the visualization of general relativity. This enables us to interactively explore the physical aspects and optical effects of Gödels universe. We also demonstrate how the analytical solution enables dynamic lighting with local illumination models. Our implementation is tailored for Gödels universe and five orders of magnitude faster than previous approaches. It can be adapted to manifolds for which an analytical expression of the propagation of light is available.

Visiting the Gödel Universe

Visualization of general relativity illustrates aspects of Einsteins insights into the curved nature of space and time to the expert as well as the layperson. One of the most interesting models which came up with Einsteins theory was developed by Kurt Godel in 1949. The Godel universe is a valid solution of Einsteins field equations, making it a possible physical description of our universe. It offers remarkable features like the existence of an optical horizon beyond which time travel is possible. Although we know that our universe is not a Godel universe, it is interesting to visualize physical aspects of a world model resulting from a theory which is highly confirmed in scientific history. Standard techniques to adopt an egocentric point of view in a relativistic world model have shortcomings with respect to the time needed to render an image as well as difficulties in applying a direct illumination model. In this paper we want to face both issues to reduce the gap between common visualization standards and relativistic visualization. We will introduce two techniques to speed up recalculation of images by means of preprocessing and lookup tables and to increase image quality through a special optimization applicable to the Godel universe. The first technique allows the physicist to understand the different effects of general relativity faster and better by generating images from existing datasets interactively. By using the intrinsic symmetries of Godels spacetime which are expressed by the Killing vector field, we are able to reduce the necessary calculations to simple cases using the second technique. This even makes it feasible to account for a direct illumination model during the rendering process. Although the presented methods are applied to Godels universe, they can also be extended to other manifolds, for example light propagation in moving dielectric media. Therefore, other areas of research can benefit from these generic improvements.

Wavefronts and Light Cones for Kerr Spacetimes

We investigate the light propagation by means of simulations of wavefronts and light cones for Kerr spacetimes. Simulations of this kind give us a new insight to better understand the light propagation in presence of massive rotating black holes. A relevant result is that wavefronts are backscattered with winding around the black hole. To generate these visualizations, an interactive computer program with a graphical user interface, called JWFront, was written in Java.

An updated version of the Motion4D-library

We present an updated version of the Motion4D-library that can be used for the newly developed GeodesicViewer application.