EXTENSION PROGRAMS ON THE SOIL BANK

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Spatially Averaged Quantum Inequalities Do Not Exist in Four-Dimensional Spacetime

We construct a particular class of quantum states for a massless, minimally coupled free scalar field which are of the form of a superposition of the vacuum and multi-mode two-particle states. These states can exhibit local negative energy densities. Furthermore, they can produce an arbitrarily large amount of negative energy in a given region of space at a fixed time. This class of states thus provides an explicit counterexample to the existence of a spatially averaged quantum inequality in four-dimensional spacetime.Comment: 13 pages, 1 figure, minor corrections and added comment

The Quantum Interest Conjecture

Although quantum field theory allows local negative energy densities and fluxes, it also places severe restrictions upon the magnitude and extent of the negative energy. The restrictions take the form of quantum inequalities. These inequalities imply that a pulse of negative energy must not only be followed by a compensating pulse of positive energy, but that the temporal separation between the pulses is inversely proportional to their amplitude. In an earlier paper we conjectured that there is a further constraint upon a negative and positive energy delta-function pulse pair. This conjecture (the quantum interest conjecture) states that a positive energy pulse must overcompensate the negative energy pulse by an amount which is a monotonically increasing function of the pulse separation. In the present paper we prove the conjecture for massless quantized scalar fields in two and four-dimensional flat spacetime, and show that it is implied by the quantum inequalities.Comment: 17 pages, Latex, 3 figures, uses eps

Weak energy condition violation and superluminal travel

Recent solutions to the Einstein Field Equations involving negative energy densities, i.e., matter violating the weak-energy-condition, have been obtained, namely traversable wormholes, the Alcubierre warp drive and the Krasnikov tube. These solutions are related to superluminal travel, although locally the speed of light is not surpassed. It is difficult to define faster-than-light travel in generic space-times, and one can construct metrics which apparently allow superluminal travel, but are in fact flat Minkowski space-times. Therefore, to avoid these difficulties it is important to provide an appropriate definition of superluminal travel.Comment: 15 pages, 3 figures, LaTeX2e, Springer style files -included. Contribution to the Proceedings of the Spanish Relativity Meeting-2001 (Madrid, September 2001

Quantum inequalities for the free Rarita-Schwinger fields in flat spacetime

Using the methods developed by Fewster and colleagues, we derive a quantum inequality for the free massive spin-${3\over 2}$ Rarita-Schwinger fields in the four dimensional Minkowski spacetime. Our quantum inequality bound for the Rarita-Schwinger fields is weaker, by a factor of 2, than that for the spin-${1\over 2}$ Dirac fields. This fact along with other quantum inequalities obtained by various other authors for the fields of integer spin (bosonic fields) using similar methods lead us to conjecture that, in the flat spacetime, separately for bosonic and fermionic fields, the quantum inequality bound gets weaker as the the number of degrees of freedom of the field increases. A plausible physical reason might be that the more the number of field degrees of freedom, the more freedom one has to create negative energy, therefore, the weaker the quantum inequality bound.Comment: Revtex, 11 pages, to appear in PR

Energy conditions, traversable wormholes and dust shells

Firstly, we review the pointwise and averaged energy conditions, the quantum inequality and the notion of the ``volume integral quantifier'', which provides a measure of the ``total amount'' of energy condition violating matter. Secondly, we present a specific metric of a spherically symmetric traversable wormhole in the presence of a generic cosmological constant, verifying that the null and the averaged null energy conditions are violated, as was to be expected. Thirdly, a pressureless dust shell is constructed around the interior wormhole spacetime by matching the latter geometry to a unique vacuum exterior solution. In order to further minimize the usage of exotic matter, we then find regions where the surface energy density is positive, thereby satisfying all of the energy conditions at the junction surface. An equation governing the behavior of the radial pressure across the junction surface is also deduced. Lastly, taking advantage of the construction, specific dimensions of the wormhole, namely, the throat radius and the junction interface radius, and estimates of the total traversal time and maximum velocity of an observer journeying through the wormhole, are also found by imposing the traversability conditions.Comment: 11 pages, 3 figures, Revtex

On the warp drive space-time

In this paper the problem of the quantum stability of the two-dimensional warp drive spacetime moving with an apparent faster than light velocity is considered. We regard as a maximum extension beyond the event horizon of that spacetime its embedding in a three-dimensional Minkowskian space with the topology of the corresponding Misner space. It is obtained that the interior of the spaceship bubble becomes then a multiply connected nonchronal region with closed timelike curves and that the most natural vacuum allows quantum fluctuations which do not induce any divergent behaviour of the re-normalized stress-energy tensor, even on the event (Cauchy) chronology horizon. In such a case, the horizon encloses closed timelike curves only at scales close to the Planck length, so that the warp drive satisfies the Ford's negative energy-time inequality. Also found is a connection between the superluminal two-dimensional warp drive space and two-dimensional gravitational kinks. This connection allows us to generalize the considered Alcubierre metric to a standard, nonstatic metric which is only describable on two different coordinate patchesComment: 7 pages, minor comment on chronology protection added, RevTex, to appear in Phys. Rev.