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

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.

Thin-shell wormholes with charge in F(R) gravity

“…Traversable Lorentzian wormholes are solutions of gravitational theories which have a throat that connects two regions of the same universe or two different universes [1,2]. In General Relativity, they are threaded by matter that violates the null energy condition [1][2][3][4][5]; the amount of this exotic matter can be made arbitrary small [6], but at the expense of large pressures at the throat [7].…”

“…In General Relativity, they are threaded by matter that violates the null energy condition [1][2][3][4][5]; the amount of this exotic matter can be made arbitrary small [6], but at the expense of large pressures at the throat [7]. Traversable wormholes can be constructed [2] by cutting and pasting two manifolds to form a new one, with a shell at the joining surface corresponding to the throat, where the flare-out condition is fulfilled.…”

Self-dual Lorentzian wormholes inn-dimensional Einstein gravity

“…The metric ansatz of Morris and Thorne [3] for the spacetime which describes a static Lorentzian wormhole is given by…”

“…The most striking of these properties is the violation of energy conditions. This implies that the matter that generates the wormholes is exotic [3,4,6], which means that its energy density is negative, as seen by static observers. These wormholes have no horizons and thus allow two-way passage through them.…”

“…The interest in this area was especially stimulated by the pioneering works of Morris, Thorne and Yurtsever [3,4], where static, spherically symmetric Lorentzian wormholes were defined and considered to be an exciting possibility for constructing time machine models with these exotic objects, for backward time travel (see also [5]). …”