Hyperfast travel in general relativity

Abstract

The problem is discussed of whether a traveller can reach a remote object and return back sooner than a photon would when taken into account that the traveller can partly control the geometry of his world. It is argued that under some reasonable assumptions in globally hyperbolic spacetimes the traveller cannot hasten reaching the destination. Nevertheless, it is perhaps possible for him to make an arbitrarily long round-trip within an arbitrarily short (from the point of view of a terrestrial observer) time.

Oxidised cosmic acceleration

“…But, even if such terms prevent pathologies, by repackaging all of the higher-derivative terms on one side of the field equations and the Einstein tensor on the other, we obtain an "effective" stress-energy which violates the NEC. This means that a variety of exotic solutions to Einstein's equations which require NEC-violating matter could potentially be permitted [37,38,39,40,45,46,47,48], but this must be checked on a case-by-case basis. It would be interesting if we were forced to accept the possibility of exotic solutions of Einstein's equations, or modifications to gravity, from observations that the universe is currently accelerating.…”

“…There are some rigorous formulations of this belief, where NEC violation is shown to lead to superluminal propagation, instabilities, and violations of unitarity or causality [30,31,32,33,34,35,36]. Certainly the NEC forbids a number of solutions to Einstein's equations with strange properties: traversable wormholes [37,38], superluminal "warp drives" [39,40,41,42,43,44], time machines [45,46], universes with big rip singularities [47,48], and pathologies with gravitational thermodynamics [49,50,51,52,53] are possible with NECviolating "exotic" matter. 2 (If one considers non-Einstein gravity, these conclusions may differ: for example, the NEC can be violated by a scalar field in Brans-Dicke gravity in Jordan frame [54] without allowing wormholes [55]).…”

Quantum effects in warp drives

“…Moreover, whereas former attempts to tackle the issue of chronology protection deeply relied on local Lorentz invariance [35], the present result suggests that this conjecture may be valid also for quantum field theories violating Lorentz invariance in the ultraviolet sector. It would be interesting to check whether all these results are general by applying a similar stability analysis to other spacetimes allowing superluminal travel, such as the Krasnikov tube [36,37].…”

A `warp drive' with more reasonable total energy requirements

“…Note that the definition does not restrict the energy-momentum tensor in S. Such spacetimes will violate at least one of the energy conditions (the weak energy condition or WEC). In the case of the Alcubierre spacetime, the situation is even worse: part of the energy in region S is moving tachyonically [2,10]. The 'Krasnikov tube' [2] was an attempt to improve on the Alcubierre geometry.…”

“…In recent years, ways of effective superluminal travel (EST) within general relativity have generated a lot of attention [1,2,3,4,5]. In the simplest definition of superluminal travel, one has a spacetime with a Lorentzian metric that is Minkowskian except for a localized region S. When using coordinates such that the metric is diag(−1, 1, 1, 1) in the Minkowskian region, there should be two points (t 1 , x 1 , y, z) and (t 2 , x 2 , y, z) located outside S, such that x 2 − x 1 > t 2 − t 1 , and a causal path connecting the two.…”