Dr. Ken D. Olum

Tufts University
Does General Relativity Permit Exotic Phenomena

Is it possible to create a stable wormhole, or to travel faster than light or backward in time? General relativity indeed in principle allows space-time to be curved into configurations which permit such things, if we can construct the appropriate states of matter and energy whose gravity would produce the desired curvature. These states all require unusual matter with negative energy density, but that by itself does not rule them out, because negative energy densities are known, for example between parallel plates in the Casimir effect. But these exotic phenomena require more than just any kind of negative energy; they require that the total energy density be negative when we add up all contributions over the complete path of a light ray. The goal of this work is to prove that this total can never be negative, or never sufficiently negative to allow for exotic phenomena, and thus that faster-than-light travel and backward time travel are impossible.

Does semi-classical gravity permit stable wormholes, faster-than-light travel, or the construction of time machines? With arbitrary matter sources, general relativity allows all these exotic phenomena, but they would be ruled out if all quantum fields obeyed the averaged null energy condition (ANEC).

First we will prove ANEC for free fields in flat space with boundaries, using recent work by Fewster and Pfenning. This work can be used to show that empty space energy conditions apply also in an empty region as long as a signal cannot travel from the region to any boundary and return to the region. This is the case for a null geodesic in flat space-time, so the argument can prove ANEC in this case.

Then we will extend the argument to interacting fields and to curved space-time. In curved space, violations of ANEC are known, but the degree of known violation is insufficient for exotic phenomena, except if the curvature is near the Planck scale, where semi-classical gravity is not applicable. By proving that curved-space violation is always insufficient, we can rule out these exotic phenomenon in semi-classical gravity.

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