Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity

TLDR

The paper introduces spacetime wormholes as a pedagogical tool for teaching general relativity, referencing Carl Sagan’s novel Contact and noting common objections to black‑hole or Schwarzschild wormholes for rapid interstellar travel. The authors derive a new class of Einstein‑field‑equation solutions in which a horizon‑free throat requires an exotic material with radial tension τ₀ ≳ (pressure at the center of the most massive neutron star)×(20 km)²/(circumference of throat)² that exceeds its mass‑energy density ρ₀c². These solutions describe wormholes that, in principle, could be traversed by human beings.

Abstract

Rapid interstellar travel by means of spacetime wormholes is described in a way that is useful for teaching elementary general relativity. The description touches base with Carl Sagan’s novel Contact, which, unlike most science fiction novels, treats such travel in a manner that accords with the best 1986 knowledge of the laws of physics. Many objections are given against the use of black holes or Schwarzschild wormholes for rapid interstellar travel. A new class of solutions of the Einstein field equations is presented, which describe wormholes that, in principle, could be traversed by human beings. It is essential in these solutions that the wormhole possess a throat at which there is no horizon; and this property, together with the Einstein field equations, places an extreme constraint on the material that generates the wormhole’s spacetime curvature: In the wormhole’s throat that material must possess a radial tension τ0 with the enormous magnitude τ0∼ (pressure at the center of the most massive of neutron stars)×(20 km)2/(circumference of throat)2. Moreover, this tension must exceed the material’s density of mass-energy, ρ0c2. No known material has this τ0>ρ0c2 property, and such material would violate all the ‘‘energy conditions’’ that underlie some deeply cherished theorems in general relativity. However, it is not possible today to rule out firmly the existence of such material; and quantum field theory gives tantalizing hints that such material might, in fact, be possible.