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Gravitational Lensing by Spinning Black Holes in Astrophysics, and the Movie Interstellar

According to James et al. Interstellar is the first movie that has attempted to depict a black hole as it would actually be seen by someone nearby. Kip Thorne, a physicist, collaborated with the team from Double Negative Visual Effects to develop a code called DNGR (Double Negative Gravitation Renderer) to solve the equations for ray-bundle (light-beam) propagation through the curved spacetime of a spinning (Kerr) black hole, as well as to render rapidly changing images that were of IMAX quality. For achieving IMAX quality smoothness without flickering their ray-bundle technique was crucial; and they are different from image-generating techniques of physicists, which are generally reliant on individual light rays rather than ray bundles), and are also different from techniques that had been used previously in the film industry’s CGI community.

There are 4 purposes for this paper:

1)      To describe DNGR for physicists and CGI practitioners.

2)      To present the equations they used when the camera is in arbitrary motion at an arbitrary location near a Kerr black hole, in order to map light sources to camera images via elliptical ray bundles.

3)      To describe new insights, from DNGR, into gravitational lensing when the camera is near the spinning black hole, instead of far away, as it is in nearly all previous studies; they focused on the shapes, sizes and influence of caustics and critical curves, the formation and annihilation of stellar images, the pattern of multiple images, and the influence of light rays that are almost trapped, and they find similar results to the case of a camera that is far from the hole that is more familiar.

4)      To describe how, in the movie Interstellar, the black hole Gargantua and its accretion disk were generated with DNGR, especially including the influences of (a) colour changes due to Doppler and gravitational frequency shifts, (b) intensity changes due to the frequency shifts, (c) camera lens flare that was simulated, and (d) decisions made by the film makers about these influences and about the spin of Gargantua, in order to produce images that were understandable to a mass audience.  In this accretion disc section of the paper there are no astrophysical insights, though disc novices may find it pedagogically interesting, and movie buffs may find interesting its discussions of Interstellar.

A thorough analytical analysis of null geodesics (light-ray propagation) around a spinning black hole was carried out in 1972 by James Bardeen; and as part of the analysis he computed how the shape of the shadow that is cast by the black hole on the light from a distant star filed. On the side of the black hole that is moving away from the observer the shadow bulges out, and squeezes inwards on the side that is moving towards the observer. For a maximally spinning black hole that is viewed from far away the result is a D-shaped shadow. The flat edge of the shadow has a notch cut out of it when it is viewed close up.

Gravitational lensing by black holes remained a backwater of research in physics for several decades, in spite of this early work, until the prospect of observations brought it to the fore again.

Sources & Further reading

  1. Oliver, J., T. Eugénie von, F. Paul and S. T. Kip (2015). "Gravitational lensing by spinning black holes in astrophysics, and in the movie Interstellar." Classical and Quantum Gravity 32(6): 065001.


Author: M. H. Monroe
Last Updated 26/07/2016
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