Gravitational lensing by spinning black holes in astrophysics, and in the movie Interstellar

Abstract

Interstellar is the first Hollywood movie to attempt depicting a black hole as it would actually be seen by somebody nearby. For this, our team at Double Negative Visual Effects, in collaboration with physicist Kip Thorne, developed a code called DNGR (Double Negative Gravitational Renderer) to solve the equations for ray-bundle (light-beam) propagation through the curved spacetime of a spinning (Kerr) black hole, and to render IMAX-quality, rapidly changing images. Our ray-bundle techniques were crucial for achieving IMAX-quality smoothness without flickering; and they differ from physicists' image-generation techniques (which generally rely on individual light rays rather than ray bundles), and also differ from techniques previously used in the film industry's CGI community.This paper has four purposes: (i) To describe DNGR for physicists and CGI practitioners, who may find interesting and useful some of our unconventional techniques. (ii) To present the equations we use, when the camera is in arbitrary motion at an arbitrary location near a Kerr black hole, for mapping light sources to camera images via elliptical ray bundles. (iii) To describe new insights, from DNGR, into gravitational lensing when the camera is near the spinning black hole, rather than far away as in almost all prior studies; we focus on the shapes, sizes and influence of caustics and critical curves, the creation and annihilation of stellar images, the pattern of multiple images, and the influence of almost-trapped light rays, and we find similar results to the more familiar case of a camera far from the hole. (iv) To describe how the images of the black hole Gargantua and its accretion disk, in the movie Interstellar, were generated with DNGR-including, especially, the influences of (a) colour changes due to doppler and gravitational frequency shifts, (b) intensity changes due to the frequency shifts, (c) simulated camera lens flare, and (d) decisions that the film makers made about these influences and about the Gargantua's spin, with the goal of producing images understandable for a mass audience. There are no new astrophysical insights in this accretion-disk section of the paper, but disk novices may find it pedagogically interesting, and movie buffs may find its discussions of Interstellar interesting.

Visualizing Interstellar's Wormhole

“…This is the same behavior as occurs with the Einstein ring of a black hole (see, e.g., Fig. 2 of our paper on black-hole lensing 12 ) and any other spherical gravitational lens, and it is also responsible for long, lenticular images of distant galaxies gravitationally lensed by a more nearby galaxy. 22 Students, having explored the wormhole's Einstein ring in a DVD or trailer of the movie, could be encouraged to go learn about Einstein rings and/or figure out for themselves how these peculiar star motions are produced.…”

“…Elsewhere 12 we describe the simulation code that we wrote for this project-DNGR for "Double Negative Gravitational Renderer"-and the black-hole and accretiondisk images we generated with it, and also some new insights into gravitational lensing by black holes that it has revealed. In this paper, we focus on wormholes, which are much easier to model mathematically than Interstellar's fast spinning black hole, and are far more easily incorporated into elementary courses on general relativity.…”

“…To produce the IMAX images needed for Interstellar, at Double Negative we developed a much more sophisticated implementation of the map within a computer code that we call DNGR 12 (Double Negative Gravitational Renderer). In DNGR, we use ray bundles (light beams) to do the mapping rather than just light rays.…”

“…Elsewhere 12 we give some details of these various "bells and whistles" for a camera orbiting a black hole rather than a wormhole. They are essentially the same for a wormhole.…”

Gravitational lensing by black holes and the case of Sgr A*

“…The results of this interplay between physics and software have been published in Ref. 11. As stated in the paper, their exploration is a rather straightforward generalization of ideas laid out by Refs.…”