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

Oliver James,Paul Franklin,Kip S Thorne,Eugénie Von Tunzelmann

doi:10.1088/0264-9381/32/6/065001

Oliver James, Paul Franklin + Show 2 more

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https://doi.org/10.1088/0264-9381/32/6/065001

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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 Double Negative Gravitational Renderer (DNGR) 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.

Highlights

Thorne, having had a bit of experience with this kind of stuff, put together a stepby-step prescription for how to map a light ray and ray bundle from the light source to the camera’s local sky; see Appendix A.1 and Appendix A.2. He implemented his prescription in Mathematica to be sure it produced images in accord with others’ prior simulations and his own intuition. He turned his prescription over to our Double Negative team, who created the fast, high-resolution code DNGR that we describe in Section 2 and Appendix A, and created the images to be lensed: fields of stars and in some cases dust clouds, nebulae, and the accretion disk around Interstellar’s black hole, Gargantua
In Appendix A.4 we describe some details of our DNGR implementation of the ray-tracing, ray-bundle, and filtering equations; in Appendix A.5 we describe some characteristics of our code and of Double Negative’s Linux-based render-farm on which we do our computations; in Appendix A.6 we describe our DNGR modelling of accretion disks; and in Appendix A.7 we briefly compare DNGR with other film-industry CGI codes and state-of-the-art astrophysical simulation codes
In this paper we have described the code DNGR, developed at Double Negative Ltd., for creating general relativistically correct images of black holes and their accretion disks

Summary

Introduction

At a summer school in Les Houches France in summer 1972, James Bardeen [1], building on earlier work of Brandon Carter [2], initiated research on gravitational lensing by spinning black holes. Bardeen gave a thorough analytical analysis of null geodesics (light-ray propagation) around a spinning black hole; and, as part of his analysis, he computed how a black hole’s spin affects the shape of the shadow that the hole casts on light from a distant star field. The result, for a maximally spinning hole viewed from afar, is a D-shaped shadow; cf Figure 4 below. (When viewed up close, the shadow’s flat edge has a shallow notch cut out of it, as hinted by Figure 8 below.) The result, for a maximally spinning hole viewed from afar, is a D-shaped shadow; cf. Figure 4 below. (When viewed up close, the shadow’s flat edge has a shallow notch cut out of it, as hinted by Figure 8 below.)

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