Quantum Interest in (3+1) dimensional Minkowski space

The so-called "Quantum Inequalities", and the "Quantum Interest Conjecture", use quantum field theory to impose significant restrictions on the temporal distribution of the energy density measured by a time-like observer, potentially preventing the existence of exotic phenomena such as "Alcubierre warp-drives" or "traversable wormholes". Both the quantum inequalities and the quantum interest conjecture can be reduced to statements concerning the existence or non-existence of bound states for a certain one-dimensional quantum mechanical pseudo-Hamiltonian. Using this approach, we shall provide a simple proof of one version of the Quantum Interest Conjecture in (3+1) dimensional Minkowski space.Comment: V1: 8 pages, revtex4; V2: 10 pages, some technical changes in details of the argument, no change in physics conclusions, this version essentially identical to published versio

Analogue model for quantum gravity phenomenology

So called "analogue models" use condensed matter systems (typically hydrodynamic) to set up an "effective metric" and to model curved-space quantum field theory in a physical system where all the microscopic degrees of freedom are well understood. Known analogue models typically lead to massless minimally coupled scalar fields. We present an extended "analogue space-time" programme by investigating a condensed-matter system - in and beyond the hydrodynamic limit - that is in principle capable of simulating the massive Klein-Gordon equation in curved spacetime. Since many elementary particles have mass, this is an essential step in building realistic analogue models, and an essential first step towards simulating quantum gravity phenomenology. Specifically, we consider the class of two-component BECs subject to laser-induced transitions between the components, and we show that this model is an example for Lorentz invariance violation due to ultraviolet physics. Furthermore our model suggests constraints on quantum gravity phenomenology in terms of the "naturalness problem" and "universality issue".Comment: Talk given at 7th Workshop on Quantum Field Theory Under the Influence of External Conditions (QFEXT 05), Barcelona, Catalonia, Spain, 5-9 Sep 200

Tolman mass, generalized surface gravity, and entropy bounds

In any static spacetime the quasi-local Tolman mass contained within a volume can be reduced to a Gauss-like surface integral involving the flux of a suitably defined generalized surface gravity. By introducing some basic thermodynamics and invoking the Unruh effect one can then develop elementary bounds on the quasi-local entropy that are very similar in spirit to the holographic bound, and closely related to entanglement entropy.Comment: V1: 4 pages. Uses revtex4-1; V2: Three references added; V3: Some notational changes for clarity; introductory paragraph rewritten; no physics changes. This version accepted for publication in Physical Review Letter

Thin-shell wormholes: Linearization stability

The class of spherically-symmetric thin-shell wormholes provides a particularly elegant collection of exemplars for the study of traversable Lorentzian wormholes. In the present paper we consider linearized (spherically symmetric) perturbations around some assumed static solution of the Einstein field equations. This permits us to relate stability issues to the (linearized) equation of state of the exotic matter which is located at the wormhole throat.Comment: 4 pages; ReV_TeX 3.0; one postscript figur

Comment on "Relativistic Effects of Light in Moving Media with Extremely Low Group Velocity"

In [cond-mat/9906332; Phys. Rev. Lett. 84, 822 (2000)] and [physics/9906038; Phys. Rev. A 60, 4301 (1999)] Leonhardt and Piwnicki have presented an interesting analysis of how to use a flowing dielectric fluid to generate a so-called "optical black hole". Qualitatively similar phenomena using acoustical processes have also been much investigated. Unfortunately there is a subtle misinterpretation in the Leonhardt-Piwnicki analysis regarding these "optical black holes": While it is clear that "optical black holes" can certainly exist as theoretical constructs, and while the experimental prospects for actually building them in the laboratory are excellent, the particular model geometries that Leonhardt and Piwnicki write down as alleged examples of "optical black holes" are in fact not black holes at all.Comment: one page comment, uses ReV_TeX 3; discussion clarified; basic physical results unaltere

Cosmography: Cosmology without the Einstein equations

How much of modern cosmology is really cosmography? How much of modern cosmology is independent of the Einstein equations? (Independent of the Friedmann equations?) These questions are becoming increasingly germane -- as the models cosmologists use for the stress-energy content of the universe become increasingly baroque, it behoves us to step back a little and carefully disentangle cosmological kinematics from cosmological dynamics. The use of basic symmetry principles (such as the cosmological principle) permits us to do a considerable amount, without ever having to address the vexatious issues of just how much "dark energy", "dark matter", "quintessence", and/or "phantom matter" is needed in order to satisfy the Einstein equations. This is the sub-sector of cosmology that Weinberg refers to as "cosmography", and in this article I will explore the extent to which cosmography is sufficient for analyzing the Hubble law and so describing many of the features of the universe around us.Comment: 7 pages; uses iopart.cls setstack.sty. Based on a talk presented at ACRGR4, the 4th Australasian Conference on General Relativity and Gravitation, Monash University, Melbourne, January 2004. To appear in the proceedings, in General Relativity and Gravitatio

Gravitational vacuum polarization III: Energy conditions in the (1+1) Schwarzschild spacetime

Building on a pair of earlier papers, I investigate the various point-wise and averaged energy conditions for the quantum stress-energy tensor corresponding to a conformally-coupled massless scalar field in the in the (1+1)-dimensional Schwarzschild spacetime. Because the stress-energy tensors are analytically known, I can get exact results for the Hartle--Hawking, Boulware, and Unruh vacua. This exactly solvable model serves as a useful sanity check on my (3+1)-dimensional investigations wherein I had to resort to a mixture of analytic approximations and numerical techniques. Key results in (1+1) dimensions are: (1) NEC is satisfied outside the event horizon for the Hartle--Hawking vacuum, and violated for the Boulware and Unruh vacua. (2) DEC is violated everywhere in the spacetime (for any quantum state, not just the standard vacuum states).Comment: 7 pages, ReV_Te

Tolman wormholes violate the strong energy condition

For an arbitrary Tolman wormhole, unconstrained by symmetry, we shall define the bounce in terms of a three-dimensional edgeless achronal spacelike hypersurface of minimal volume. (Zero trace for the extrinsic curvature plus a "flare-out" condition.) This enables us to severely constrain the geometry of spacetime at and near the bounce and to derive general theorems regarding violations of the energy conditions--theorems that do not involve geodesic averaging but nevertheless apply to situations much more general than the highly symmetric FRW-based subclass of Tolman wormholes. [For example: even under the mildest of hypotheses, the strong energy condition (SEC) must be violated.] Alternatively, one can dispense with the minimal volume condition and define a generic bounce entirely in terms of the motion of test particles (future-pointing timelike geodesics), by looking at the expansion of their timelike geodesic congruences. One re-confirms that the SEC must be violated at or near the bounce. In contrast, it is easy to arrange for all the other standard energy conditions to be satisfied.Comment: 8 pages, ReV-TeX 3.

Geometric structure of the generic static traversable wormhole throat

Traversable wormholes have traditionally been viewed as intrinsically topological entities in some multiply connected spacetime. Here, we show that topology is too limited a tool to accurately characterize a generic traversable wormhole: in general one needs geometric information to detect the presence of a wormhole, or more precisely to locate the wormhole throat. For an arbitrary static spacetime we shall define the wormhole throat in terms of a 2-dimensional constant-time hypersurface of minimal area. (Zero trace for the extrinsic curvature plus a "flare-out" condition.) This enables us to severely constrain the geometry of spacetime at the wormhole throat and to derive generalized theorems regarding violations of the energy conditions-theorems that do not involve geodesic averaging but nevertheless apply to situations much more general than the spherically symmetric Morris-Thorne traversable wormhole. [For example: the null energy condition (NEC), when suitably weighted and integrated over the wormhole throat, must be violated.] The major technical limitation of the current approach is that we work in a static spacetime-this is already a quite rich and complicated system.Comment: 25 pages; plain LaTeX; uses epsf.sty (four encapsulated postscript figures