December 18, 1998
Some standard results on the initial value problem of general relativity in matter are reviewed. These results are applied first to show that in a well defined sense, finite perturbations in the gravitational field travel no faster than light, and second to show that it is impossible to construct a warp drive as considered by Alcubierre (1994) in the absence of exotic matter.
April 5, 2022
For many years now it has become conventional for theorists to argue that "space-time is doomed", with the difficulties in finding a quantum theory of gravity implying the necessity of basing a fundamental theory on something quite different than usual notions of space-time geometry. But what is this space-time geometry that is doomed? In this essay we'll explore how our understanding of four-dimensional geometry has evolved since Einstein, leading to new ideas about such geo...
November 13, 2023
Presented are toy-models for sub-luminal and super-luminal warp-drives in 3+1 dimensions. The models are constructed in a chimeric manner - as different bulk space-times separated by thin membranes. The membranes contain perfect-fluid-like stress-energy tensors. The Israel junction conditions relate this stress-energy to a jump in extrinsic curvature across the brane, which in turn manifests as apparent acceleration in the bulk space-times. The acceleration on either side of ...
April 11, 1999
Coule's primary objection to the Alcubierre "warpdrive" is that the material producing the warp field needs to be superluminal. This difficulty is solved by placing the drive material inside its own warp field (making the drive system part of the payload), but we then have to deal with Low's related objection, that there is then a restricted rate at which this "naked" warp-field can propagate through the background metric. We argue that the propagation of this sort of gravita...
September 1, 2004
A `quantum inequality' (a conjectured relation between the energy density of a free quantum field and the time during which this density is observed) has recently been used to rule out some of the macroscopic wormholes and warp drives. I discuss the possibility of generalizing that result to other similar spacetimes and first show that the problem amounts to verification of a slightly different inequality. This new inequality \emph{can} replace the original one, if an additio...
July 28, 2011
The Alcubierre warp spacetime yields a fascinating chance for comfortable interstellar travel between arbitrary distant places without the time dilation effect as in special relativistic flights. Even though the warp spacetime needs exotic matter for its construction and is thus far from being physically feasible, it offers a rich playground for studying geodesics in the general theory of relativity. This paper is addressed to graduate students who have finished a first cours...
August 18, 2012
We present an analysis of the classic Alcubierre metric based on conformal gravity, rather than standard general relativity. The main characteristics of the resulting warp drive remain the same as in the original study by Alcubierre, namely that effective super-luminal motion is a viable outcome of the metric. We show that for particular choices of the shaping function, the Alcubierre metric in the context of conformal gravity does not violate the weak energy condition, as wa...
May 20, 1998
Since the shape of a free body's worldline is determined by the geometry of spacetime a local change of spacetime geometry will affect a body's worldline, i.e. a body's state of motion. The exploration of this possibility constitutes a radically new approach to the idea of how a body can be propelled: instead of applying a force to the body itself, the geometry of spacetime is subjected to a local manipulation which in turn results in the body's motion.
May 4, 2024
Warp drives are exotic solutions of general relativity that offer novel means of transportation. In this study, we present a solution for a constant-velocity subluminal warp drive that satisfies all of the energy conditions. The solution involves combining a stable matter shell with a shift vector distribution that closely matches well-known warp drive solutions such as the Alcubierre metric. We generate the spacetime metric numerically, evaluate the energy conditions, and co...
February 9, 2021
The Alcubierre warp drive metric is a spacetime construction where a massive particle located inside a spacetime distortion, called warp bubble, travels at velocities arbitrarily higher than the velocity of light. This theoretically constructed spacetime geometry is a consequence of general relativity where global superluminal velocities, also known as warp speeds, are possible, whereas local speeds are limited to subluminal ones as required by special relativity. In this wor...