Tufts/CfA/MIT Cosmology Seminar, at Tufts:

                      Tuesday March 4, 1997
                             2:30 pm
                         Robinson Hall, Rm. 153

             "Warp Bubbles, Warp Tubes, and Time Machines"

                           Allen Everett
                          Tufts University

Abstract: 
Alcubierre showed recently, with a specific example, that it is 
possible, within the framework of general relativity, to warp spacetime 
in a small bubblelike region in such a way that a space ship within the 
bubble can move with with arbitrarily large speed relative to observers 
in flat space outside the bubble.  The corresponding energy-momentum 
tensor involves regions of negative energy density, i. e., a violation of 
the weak energy condition.  The occurrence of regions of negative energy 
density is allowed in quantum field theory.  However, Ford and Roman have 
proved inequalities, called quantum inequalities, which limit the 
magnitude and duration of negative energy density, and Pfenning and Ford 
have applied these to show that the possibility of establishing 
Alcubierre bubbles appears remor.
   After a brief review of Alcubierre's "warp drive" metric, I will 
discuss work done in collaboration with Tom Roman in which an alternative 
metric proposed by Krasnikov is analysed in detail and generalized from 2 
to 4 dimensions.  Alcubierre's metric has the problem that an observer at 
the center of a "warp bubble" is out of causal contact with parts of the 
outer edge of the bubble wall, and hence cannot create or control the 
bubble.  Krasnikov's metric does not share this problem, and one might 
hope that as a result the negative energy problem might also be 
alleviated.  The Krasnikov metric has the interesting property that, 
although the one-w-travel time to a star at a distance D cannot be less 
than D/c, the time for a round trip, as measured by clocks either on the 
earth of the ship, can in principle be arbitrarily short.  In the work to 
be described, the Krasnikov metric is generalized from 2 to 4 
spacetime dimensions;  in 4 dimensions it describes the creation of 
"tubes" within which the light cone is "opened out" to allow superluminal 
travel in one direction.  We show that, as shown previously for the 
Alcubierre metric, the existence of closed timelike curves is possible;  
their existence requires a combination of two nonoverlapping Krasnikov 
tubes oriented in opposite directions.  Finally we obtain the 
stress-energy tensor for a Krasnikov tube and show, both analytically 
and numerically, that the negative energy problems encountered are 
comparable to those found for the Alcubierre metric.  The quantum 
inequalities are applied, and they suggest strongly that Krasnikov tubes 
cannot be realized in practice.