Superluminal subway: The Krasnikov tube

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 56, Issue 4, 1997, Pages 2100-2108

  Everett, Allen E ^a   Roman, Thomas A ^a  

^a TUFTS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000214969     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.56.2100     Document Type: Article

References (24)

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12. S. V. Krasnikov, “Hyper-Fast Interstellar Travel in General Relativity,” Report No. (unpublished).
13. A similar argument has been given by M. Pfenning (unpublished).
14. M. Visser, Lorentzian Wormholes—from Einstein to Hawking (American Institute of Physics Press, New York, 1995).
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17. M. Pfenning and L. H. Ford (unpublished).
18. See, for example, Sec. 5.6 of B. Schutz, A First Course in General Relativity (Cambridge University Press, Cambridge, England, 1985).
19. The specific form of (Formula presented) chosen here has the minor drawback that the numerical value of (Formula presented) does not quite go exactly to zero at (Formula presented) (as it must by symmetry), although it does become very small. The resulting apparent “singularity” in (Formula presented) at (Formula presented) can be remedied by using a somewhat more cumbersome form of (Formula presented) with an additional term which has the effect of forcing (Formula presented) at (Formula presented). Since this added complication changes neither our results nor our conclusion, while tending to obscure the physical interpretation of (Formula presented), we have chosen to use the simpler form.
20. The apparent singularity in (Formula presented) when (Formula presented) is related to the problem at (Formula presented) mentioned in the previous reference. It arises because for (Formula presented), we are evaluating (Formula presented) at (Formula presented).
21. From the results of Ref. 10, our conclusion will be the same if we construct the Krasnikov tube out of quantized massive scalar or electromagnetic fields.
22. We assumed for simplicity that the values of the (Formula presented)’s in all of the (Formula presented) functions were equal. Relaxation of this assumption would make the model more complicated but should not, we believe, change the essential result. That is, in the latter case as well, we expect that (although we have not proven it) at least one of the (Formula presented)’s appearing in the expression for (Formula presented) will be constrained by the quantum inequality to be exceedingly small.
23. Of course the total energy (matter plus gravitational) of the Krasnikov tube, as measured by observers at infinity, is zero since the external metric is Minkowskian.
24. The authors are grateful to Larry Ford for suggesting several key parts of this argument.