Visualizing Interstellar's Wormhole

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 lightray-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 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.

Wormhole geometries in fourth-order conformal Weyl gravity

“…(7), for Φ(l) = 0 and r(l) = b 2 0 + l 2 . This metric was later re-introduced and generalized by Morris-Thorne [1] in 1988, used as a tool for teaching general relativity by J. Hartle [39], visualized in various environments by Müller et al [40], and recently revisited by Thorne et al [41] after being popularized by the science fiction movie Interstellar.…”

Traversable wormholes and non-singular black holes from the vacuum of quadratic gravity

“…Imposing such conditions prohibits the construction of many spacetimes in the context of GR, including traversable wormholes [6]. Wormholes have appeared in many science fiction settings, recently giving rise to additional research on the subject [7]. Besides a means of rapid interstellar travel used by advanced civilizations, wormholes are discussed in the quest to understand the relation between entanglement and the possible emergence of spacetime [8].…”

Simple perturbatively traversable wormholes from bulk fermions

“…The expectation value of the Belinfante stress-energy tensor in terms of the spinor propagator is [30] T µν = i 2 lim where a primed index on the covariant derivative denotes a derivative on the second coordinate and action from the left. The parallel propagators become trivial at coincident 6 For timelike geodesics, we would instead make the same substitutions as in [32], with z ≡ cos 2 s 2 . 7 For a similar calculation in AdS4 for timelike geodesics, see [35] points, namely g ν ν = δ ν ν and Λ(x, x ) = I 2 at x = x .…”

“…Wormholes have long been a source of fascination both in the scientific literature [1][2][3][4][5] and in science fiction [6] as a potential tool for producing superluminal travel. In classical general relativity, wormholes are nontraversable due to constraints on causality from the null energy condition (NEC), which implies the topological censorship theorems [7,8].…”