Visualizing Interstellar's Wormhole

TL;DR

This paper explores how elementary relativity concepts can be used to visualize and understand wormholes as depicted in the movie Interstellar, combining educational calculations, light-ray tracing, and parameter exploration.

Contribution

It introduces a step-by-step educational approach to visualize wormholes, including computational methods and parameter analysis inspired by the movie's visual effects.

Findings

Constructed embedding diagrams for wormholes.

Developed light-ray-tracing maps for wormhole visualization.

Explored star motions and Einstein rings near wormholes.

Abstract

Christopher Nolan's science fiction movie Interstellar offers a variety of opportunities for students in elementary courses on general relativity theory. This paper describes such opportunities, including: (i) At the motivational level, the manner in which elementary relativity concepts underlie the wormhole visualizations seen in the movie. (ii) At the briefest computational level, instructive calculations with simple but intriguing wormhole metrics, including, e.g., constructing embedding diagrams for the three-parameter wormhole that was used by our visual effects team and Christopher Nolan in scoping out possible wormhole geometries for the movie. (iii) Combining the proper reference frame of a camera with solutions of the geodesic equation, to construct a light-ray-tracing map backward in time from a camera's local sky to a wormhole's two celestial spheres. (iv) Implementing this map, for example in Mathematica, Maple or Matlab, and using that implementation to construct images of what a camera sees when near or inside a wormhole. (v) With the student's implementation, exploring how the wormhole's three parameters influence what the camera sees---which is precisely how Christopher Nolan, using our implementation, chose the parameters for \emph{Interstellar}'s wormhole. (vi) Using the student's implementation, exploring the wormhole's Einstein ring, and particularly the peculiar motions of star images near the ring; and exploring what it looks like to travel through a wormhole.