The Double Negative Gravitational Renderer (DNGR) is the computer code used to create the iconic images of black holes and wormholes for the movie Interstellar.

It is the result of a year-long collaboration between Professor Kip Thorne and Double Negative Chief Scientist Oliver James, leading a small team of developers.

DNGR uses general-relativity equations to trace beams of light as they are bent and warped by the immense gravity of a black hole. Beams can get temporarily trapped, circling the hole many times before reaching the camera. These beams’ cross sections get stretched and squashed during this process, amplifying the light in small regions, resulting in glittering patterns in the starlight; and thin accretion discs get warped into rainbows of fire that stretch over and under the black hole.

The unprecedented detail DNGR reveals has led to its use as a tool for astrophysics research, giving us new insights into gravitational lensing.

Below you will find images and movies discussed in our paper ‘Gravitational Lensing by Spinning Black Holes in Astrophysics, and in the Movie Interstellar’ which is available for free download here:

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

Published by IoP in Classical and Quantum Gravity James O, von Tunzelmann E, Franklin P and Thorne K S 2015 Class. Quantum Grav. 32 065001

(Also of interest may be our technical paper ‘Visualizing Interstellar’s Wormhole’)

All these movies entail a black hole with spin 0.999 of maximum and a camera at radii  6.03 GM/c2 or 2.6 GM/c2, where M is the black hole’s mass, and G and c are Newton’s gravitational constant and the speed of light. The observer is moving in a circular geodesic orbit.

View of a starfield under the influence of gravitational lensing. The camera is at radius r=2.6 GM/c2

View of a starfield under the influence of gravitational lensing. The camera is at radius r=6.03 GM/c2

View of a starfield under the influence of gravitational lensing. The camera is at radius r=6.03 GM/c2. The primary and secondary critical curves are overlaid in purple and the path of a star at polar angle 0.608 pi is overlaid in red.

For a camera at radius rc = 6.03 GM/c2: Animation showing the mapping between points on the primary critical curve in the camera’s sky and the primary caustic curve on the celestial sphere.

For a camera at radius rc = 6.03 GM/c2: Animation showing the mapping between points on the secondary critical curve in the camera’s sky and the secondary caustic curve on the celestial sphere.

For a camera at radius rc = 2.6 GM/c2: Animation showing the mapping between points on the primary critical curve in the camera’s sky and the primary caustic curve on the celestial sphere.

For a camera at radius rc = 2.6 GM/c2: Animation showing the mapping between points on the secondary critical curve in the camera’s sky and the secondary caustic curve on the celestial sphere.

For a camera at radius rc = 2.6 GM/c2: Animation showing the mapping between points on the tertiary critical curve in the camera’s sky and the tertiary caustic curve on the celestial sphere.

DNGR development team: Oliver James, Sylvan Dieckmann, Simon Pabst, Damien Maupu, Paul-George Roberts, Shane Christopher
VFX Supervisor: Paul Franklin
CG Supervisor: Eugénie von Tunzelmann