Torus around a Schwarzschild black hole

A short manual

Introduction

For an observer moving with relativistic velocity in the vicinity of a black hole the optical appearance of objects is substantially influenced by light bending due to the black hole and aberration due to relativistic movement. Using todays high performance graphics hardware, we have developed a Qt application which enables the user to interactively explore what an observer, who moves with arbitrary velocity in a torus around the black hole, would actually see.

System requirements

You need a graphics card with an NVIDIA GeForce 7900 chip or higher and at least 300MB GPU memory or an equivalent graphics card.

Download

Before running the application you need the following material:

Installation

You need the Gnu Scientific Library gsl to run this program. Before compiling the code, set the environment variable TOP_DIR to the path of the qtTorus directory and the the environment variable GSL_DIR to the path of your gsl-installation.
Then, just run qmake and make.

Start the application

To start the application use the command
./Torus

Loading the LUT's

After the program has started, the LUT's must be loaded. To do this, click on File and load the corresponding files.

In adition to the LUT's image files for the background and the torus are required and must be loaded the same way.

If the Doppler effect shall be visualized a spectrum has to be loaded as well.

Graphical User Interface

OpenGL-window (1)

By pressing the left mouse button, you can change the line of sight.

Torus parameters panel (2)

The appearance of the torus can be modified here. The torus can either be rendered completely or parts of its surface can be discarded to get a better 3-dimensional impression. You can discard circles as well as stripes. The number of stripes is controlled by the variable ζ_factor and their thickness by ζ_part. The ψ-variables control the circles in the same manner. Furthermore, the level of transparency of the torus can be adjusted by changing the value of transp and the dimming of points by changing the value of dark. Points will be dimmed depending on the respective affine parameter in the LUT.

Motion panel (3)

Before you can start the animation you must stecify a velocity β=v/c for the observer with respect to the speed of light c. Possible values for β are in the interval [0,1), for values close to 1 however, the program might have problems to depict the situation correctly due to the large distortion. By setting τ_step you can decide which amount of proper time elapses between two pictures. To start the animation click on the play button . Clicking play again stops the visualization and clicking rewind resets the programm to the initial position

Viewing panel (4)

These options control the format of the picture itself. By defining a certain Field of View via FoVy you can either zoom in on a certain region or get a large scale impression. Possible values for FoVy are in the interval [1,120] degree?s?. Using VDir you can chose to ignore geodesic precession and always look in φ-direction. If Freq is selected, the torus image is used to calculate a temperature distribution for the torus instead of using it as a simple texture.

Temperature (5)

These options are only available if a spectrum has been loaded and if Freq is selected. Here the temperatures assigned to different points of the torus can be manipulated. For a certain RGB value in the torus image a gray value g is calculated via g=0.3R + 0.59G + 0.11B. This value is used to assign a temperature to the corresponding point on the torus via T=T_min + (g-g_offset)(T_max-Tmin)/g_slope. Thus, by increasing g_offset the temperature interval increases and by decreasing g_slope the temperature interval decreases. Possible values are [0,0.99] for g_offset and [0.01,1] for g_slope with the default values 0 for g_offset and 1 for g_slope. If no spectrum was loaded, the torus can only be displayed using the loaded torus image as such.

Other Options

Alternatively a FourPi projection can be used to simultaneously visualize the observer's entire field of view. For reference it is also possible to display the current line of sight of the observer with respect to the black hole and the current tidal accelerations he feels. To use these options click on Windows and mark the respective entry.

Contact

Visualisierungsinstitut der Universität Stuttgart, VISUS
Allmandring 19
70569 Stuttgart, Germany
Email: Thomas.Mueller@vis.uni-stuttgart.de