Abstract
“Warp drive” spacetimes and wormhole geometries are useful as “gedanken-experiments” that force us to confront the foundations of general relativity, and among other issues, to precisely formulate the notion of “superluminal” travel and communication. Here, we will consider the basic definition and properties of warp drive spacetimes. In particular, we will discuss the violation of the energy conditions associated with these spacetimes, as well as some other interesting properties such as the appearance of horizons for the superluminal case, and the possibility of using a warp drive to create closed timelike curves. Furthermore, due to the horizon problem, an observer in a spaceship cannot create nor control on demand a warp bubble. To contour this difficulty, we discuss a metric introduced by Krasnikov, which also possesses the interesting property in that the time for a round trip, as measured by clocks at the starting point, can be made arbitrarily short.
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Notes
- 1.
It is also interesting to note that the inclusion of a generic lapse function \(\alpha (x,y,z,t)\), in the metric , decreases the negative energy density , which is now given by
One may impose that \(\alpha \) may be taken as unity in the exterior and interior of the warp bubble, so that proper time equals coordinate time. In order to significantly decrease the negative energy density in the bubble walls, one may impose an extremely large value for the lapse function. However, the inclusion of the lapse function suffers from an extremely severe drawback, as proper time as measured in the bubble walls becomes absurdly large, \(d\tau =\alpha \,dt\), for \(\alpha \gg 1\).
- 2.
- 3.
Due to these results, one may tentatively conclude that the existence of these spacetimes is improbable. But, there are a series of considerations that can be applied to the QI. First, the QI is only of interest if one is relying on quantum field theory to provide the exotic matter to support the Alcubierre warp bubble. However, there are classical systems (non-minimally coupled scalar fields ) that violate the null and the weak energy conditions , whilst presenting plausible results when applying the QI (See Chap. 10). Second, even if one relies on quantum field theory to provide exotic matter , the QI does not rule out the existence of warp drive spacetimes, although they do place serious constraints on the geometry.
- 4.
See Ref. [22] for more details.
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Acknowledgements
FSNL acknowledges financial support of the Fundação para a Ciência e Tecnologia through an Investigador FCT Research contract, with reference IF/00859/2012, funded by FCT/MCTES (Portugal). MA also acknowledges support from UNAM through PAPIIT-IN103514 grant, and from CONACYT through infrastructure grant 253709.
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Alcubierre, M., Lobo, F.S.N. (2017). Warp Drive Basics. In: Lobo, F. (eds) Wormholes, Warp Drives and Energy Conditions. Fundamental Theories of Physics, vol 189. Springer, Cham. https://doi.org/10.1007/978-3-319-55182-1_11
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