General-relativistic visualization makes use of different rendering techniques. The most straightforward one is a generalization of ray tracing to four dimenions. In contrast to standard ray tracing, light rays have to follow null geodesics in the respective four-dimensional spacetime which makes this technique rather time consuming.
If there is an analytic solution to the geodesic equation, it might be possible to speed-up the rendering by utilizing the symmetry of the spacetime and by precalculating different aspects of null geodesics. It might also be possible to achieve interactive frame rates.
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Ray tracing of a black hole and its shadow
In April 2019, the first "image" of a black hole was published by the Event Horizon Telescope (EHT) scientists. In cooperation with the relativistic astrophysics group led by Luciano Rezzolla a short movie explaining how the shadow of a black hole emerges and how the distorted view of a thin accretion disk looks like was created.
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Kerr black hole with thin accretion disk
Accretion disk around Kerr black hole (a=0.7M) represented by a ring with inner radius r=4M and outer radius r=14M.
The inclination angle between the disk normal and the direction to the observer reads i=80deg.
Here, only the geometric distortion of the disk and the background is shown.
Render your own black hole using GeoViS.
The scene description file can be found here. Please note that only geometric effects are taken into account.
The Milky Way panorama is by ESO/S.Brunier.
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Black hole passing in front of the Milky Way background
A Schwarzschild black hole moves in front of the Milky Way background panorama. The movie was rendered using GeoViS. The Milky Way panorama is by ESO/S.Brunier.
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Schwarzschild black hole with non-relativistic SPH accretion disk
The disk is based on a non-relativistic Smoothed-Particle-Hydrodynamics (SPH) simulation by Roland Speith.
The apparent distortion of the disk is due to the bending of light within the Schwarzschild spacetime. Besides the primary image of the disk, there are also higher order images (lower ring and upper thin ring) visible. The lower ring shows the rear bottom side of the disk. The color encodes the apparent temperature where blue is hot and red is cold. The left part of the disk approaches the observer and, thus, appears blue-shifted.
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Reissner-Nordström dihole
The Reissner-Nordström dihole metric describes a spacetime with two black holes. Here, the black holes reside on the z-axis (z=+1 and z=-1) and a ball oscillates between them along the x-axis. (Rendered with GeoViS, scene created by Andreas Wünsch)
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Warp drive
The warp drive by Miguel Alcubierre passes in front of the Milky Way panorama and a chequered sphere. Due to the finite speed of light, two bubbles can be observed which apparently move in opposite directions.
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Visualization of a Morris-Thorne wormhole
The Morris-Thorne wormhole spacetime is one of the most simple, non-trivial solution of Einstein's General Theory of Relativity.
However, it is not so easy to understand what an observer traveling through this wormhole spacetime would actually see.
The most straight forward method to visualize the first-person view is four-dimensional ray-tracing.
Note: The spacetime geometry described in the Morris-Thorne paper should be called "Ellis wormhole" according to H. Ellis.
More details can be found here |
