Distortion of the stellar sky by a Schwarzschild black hole

Distortion of the stellar sky by a Schwarzschild black hole

Thomas Müller, Daniel Weiskopf

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.

Qt application / data files   

The application can be downloaded for Linux and Windows:

  • Linux source files can be downloaded here (gzip-compressed tar-file, 912 kB, md5: f662bf6679221a5d09470089e1a78c9f, LinuxDssBH.tgz).
    (Installation manual.)
  • Windows executable can be downloaded here (zip-archive, 6.1 MB, 2014-03-31, md5: 0df7e89e7de7d1fbde1fc4c44a4507ef, WinDssBH_20140331.zip).
    (Installation manual.)

The following data files have to be stored in the 'data' directory of the application:

  • Distortion array for the region above the horizon: array_outside.bin (binary data file, 128MB, md5: f4c0b26a09a3aefe9229bfbe0b33cfb8, array_outside.bin).
  • Distortion array for the region below the horizon: array_inside.bin (binary data file, 128MB, md5: 8173ad3018abd69191b5724947b918fb, array_inside.bin).
  • Integral psi_V as a function of temperature: psitemp.bin (binary data file, 2.1kB, md5: 39c639f33a28c05588faffae38bb4d73, psitemp.bin).
  • Color values Sigma_j: sigma.bin (binary data file, 3.1MB, md5: 33debcde6617a0dbf0c5fa7c26910c9b, sigma.bin).
  • Hipparcos catalogue: hip.bin (binary data file, 2.8MB, md5; 05009be6c43ee30a65f14c13ccceaf11, hip.bin).
  • All these data files can also be downloaded as one single tar-file (262MB, md5: 6e0e83f2c728bdfe30164e0c84e5f8cc, DataDssBH.tar).

The Hipparcos catalogue was taken from CDS. The necessary data (right ascension, declination, etc.) was stored in the binary file (hip.bin).

System requirements   

  • At least 300MB GPU memory.
  • The Linux version needs the free Qt SDK which can be found here.

The application was tested with the graphics boards: NVidia GeForce 8600 GT, ATI Radeon HD 3800.


  • ContourPlot of the integrated intensity I_V scaled by the maximum I_max




The following movies show some example situations. You should download the files before playing.

The observer is rotating around the Schwarzschild black hole on the fixed radius rObs/rs = 5.0

(mp4, 15MB)
The observer quasistatically approaches the black hole.

(mp4, 6MB)
Free fall starting with zero velocity from rObs/rs = 5.0

(mp4, 7.4MB)



  • T. Müller, D. Weiskopf
    Distortion of the stellar sky by a Schwarzschild black hole
    American Journal of Physics 78, 204-214 (2010).
    DOI: 10.1119/1.3258282


Table I: Alnilam has trigonometric parallax of 2.43 mas.


Visualisierungsinstitut der Universität Stuttgart (VISUS)
Allmandring 19
70569 Stuttgart, Germany

Email: Thomas.Mueller@vis.uni-stuttgart.de
Email: Daniel.Weiskopf@visus.uni-stuttgart.de

All contents copyright © 2010, Thomas Müller, Daniel Weiskopf
All rights reserved.