Distortion of the stellar sky by a Schwarzschild black hole

Introduction

The optical appearance of the stellar sky for an observer in the vicinity of a black hole is dominated by bending of light, frequency shift, and magnification caused by gravitational lensing and aberration. Due to the finite apperture of an observer's eye or a telescope, Fraunhofer diffraction has to be taken into account. Using todays high performance graphics hardware, we have developed a Qt application which enables the user to interactively explore the stellar sky in the vicinity of a Schwarzschild black hole. For that, we determine what an observer, who can either move quasistatically around the black hole or follow a timelike radial geodesic, would actually see.

System requirements

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

Download

• Hipparcos catalogue: hip.bin
• Lookup tables: array_inside.bin, array_outside.bin, psitemp.bin, sigma.bin

Installation

To compile DssBH by yourself, you need Qt.
Then, just run qmake and make.

Start the application

To use only stars up to magnitude Vmag = 7:
./DssBH

To use start up to magnitude Vmag, e.g.:
./DssBH 12

Note that it can take a few seconds to load the data.

Graphical User Interface

OpenGL-window (1)

The 4pi projection shows the view of the observer in all directions. The distortion on the top and the bottom of this projection is due to the mapping of spherical coordinates onto a plane surface and has nothing to do with the distortion due to the black hole. However, the advantage of this projection is to see at a glance how the complete sky will look like. By pressing the left mouse button, you can quasistatically move around the black hole on a fixed radial distance with the viewing direction always pointing towards the black hole.

Observer panel (2)

The initial position r_i of the observer for the free fall situation or the current radial distance for the quasi-static motion is scaled by the Schwarzschild radius r_s.

Position/Time panel (3)

Depending on the initial position r_i, a freely falling observer would crash into the black hole singularity within the proper time tau_crash which is scaled by the speed of light c and the Schwarzschild radius r_s. If the freely-falling-mode is activated, you can change either the current position or proper time of the falling observer by moving the sliders.

Animation (4)

Instead of moving the sliders, you can also animate the free fall where the proper time increases homogenously. The animate factor scales the time step.

Shader (5)

The output of the star simulation can be influenced by three parameters: gamma-factor, f_0, and maximum pointsize which defines the size of the Airy disc.

Howto

• Observer
  
  • Mode
    The observer can either move quasi-statically around the black hole or can fall freely on a radial timelike geodesic into the black hole
    
    
  • Initial position
    For quasi-static motion, the initial position 'r_i' fixes the radius of the observer.
    For the free fall, the observer starts with zero velocity from the initial position 'r_i'. Here, the initial position is scaled by the Schwarzschild radius 'r_s'.
  
  
• Position/Time
  
  • Crash time
    A freely falling observer starting with zero velocity from the initial position defined above, will crash into the singularity within the proper time tau. Here, the proper time is scaled by the speed of light 'c' and the Schwarzschild radius 'r_s'.
    
    
  • Current position
    In the free-fall mode, moving the slider changes the current position 'rObs' of the observer between the initial position 'r_i' and the singularity r=0.
    
    
  • Current proper time
    In the free-fall mode, moving the slider changes the current proper time 'tau' of the observer between tau=0 and the crash time 'tau_crash'.
    
    
• Animate
  
  • play
    Instead of moving the proper time slider, the 'play' button starts the free-fall animation, where the proper time of the observer increases monotonically.
    
    
  • factor
    The factor determines the relation between the oberver's proper time and the simulation time. A higher factor let's play the animation faster.
    
    
• Shader
  
  • gamma
    
  • f0
    
  • Max point size
    

Some realistic parameters

Contact