Dynamic wormholes

A new framework is proposed for general dynamic wormholes, unifying them with black holes. Both are generically defined locally by outer trapping horizons, temporal for wormholes and spatial or null for black and white holes. Thus wormhole horizons are two-way traversible, while black-hole and white-hole horizons are only one-way traversible. It follows from the Einstein equation that the null energy condition is violated everywhere on a generic wormhole horizon. It is suggested that quantum inequalities constraining negative energy break down at such horizons. Wormhole dynamics can be developed as for black-hole dynamics, including a reversed second law and a first law involving a definition of wormhole surface gravity. Since the causal nature of a horizon can change, being spatial under positive energy and temporal under sufficient negative energy, black holes and wormholes are interconvertible. In particular, if a wormhole's negative-energy source fails, it may collapse into a black hole. Conversely, irradiating a black-hole horizon with negative energy could convert it into a wormhole horizon. This also suggests a possible final state of black-hole evaporation: a stationary wormhole. The new framework allows a fully dynamical description of the operation of a wormhole for practical transport, including the back-reaction of the transported matter on the wormhole. As an example of a matter model, a Klein-Gordon field with negative gravitational coupling is a source for a static wormhole of Morris & Thorne.Comment: 5 revtex pages, 4 eps figures. Minor change which did not reach publisher

Acceleration of convergence of vector sequences

A general approach to the construction of accelerated convergence methods for vector sequences is proposed. A simplified version of minimal polynomial extrapolation is emphasized. The convergence of this method is analyzed and it is shown that it is especially suitable for accelerating the convergence of vector sequences that are obtained when one solves linear systems of equations iteratively

Cosmological and Black Hole Horizon Fluctuations

The quantum fluctuations of horizons in Robertson-Walker universes and in the Schwarzschild spacetime are discussed. The source of the metric fluctuations is taken to be quantum linear perturbations of the gravitational field. Lightcone fluctuations arise when the retarded Green's function for a massless field is averaged over these metric fluctuations. This averaging replaces the delta-function on the classical lightcone with a Gaussian function, the width of which is a measure of the scale of the lightcone fluctuations. Horizon fluctuations are taken to be measured in the frame of a geodesic observer falling through the horizon. In the case of an expanding universe, this is a comoving observer either entering or leaving the horizon of another observer. In the black hole case, we take this observer to be one who falls freely from rest at infinity. We find that cosmological horizon fluctuations are typically characterized by the Planck length. However, black hole horizon fluctuations in this model are much smaller than Planck dimensions for black holes whose mass exceeds the Planck mass. Furthermore, we find black hole horizon fluctuations which are sufficiently small as not to invalidate the semiclassical derivation of the Hawking process.Comment: 22 pages, Latex, 4 figures, uses eps

Quantum Inequalities on the Energy Density in Static Robertson-Walker Spacetimes

Quantum inequality restrictions on the stress-energy tensor for negative energy are developed for three and four-dimensional static spacetimes. We derive a general inequality in terms of a sum of mode functions which constrains the magnitude and duration of negative energy seen by an observer at rest in a static spacetime. This inequality is evaluated explicitly for a minimally coupled scalar field in three and four-dimensional static Robertson-Walker universes. In the limit of vanishing curvature, the flat spacetime inequalities are recovered. More generally, these inequalities contain the effects of spacetime curvature. In the limit of short sampling times, they take the flat space form plus subdominant curvature-dependent corrections.Comment: 18 pages, plain LATEX, with 3 figures, uses eps

Quantum inequalities in two dimensional curved spacetimes

We generalize a result of Vollick constraining the possible behaviors of the renormalized expected stress-energy tensor of a free massless scalar field in two dimensional spacetimes that are globally conformal to Minkowski spacetime. Vollick derived a lower bound for the energy density measured by a static observer in a static spacetime, averaged with respect to the observers proper time by integrating against a smearing function. Here we extend the result to arbitrary curves in non-static spacetimes. The proof, like Vollick's proof, is based on conformal transformations and the use of our earlier optimal bound in flat Minkowski spacetime. The existence of such a quantum inequality was previously established by Fewster.Comment: revtex 4, 5 pages, no figures, submitted to Phys. Rev. D. Minor correction

Scalar Field Quantum Inequalities in Static Spacetimes

We discuss quantum inequalities for minimally coupled scalar fields in static spacetimes. These are inequalities which place limits on the magnitude and duration of negative energy densities. We derive a general expression for the quantum inequality for a static observer in terms of a Euclidean two-point function. In a short sampling time limit, the quantum inequality can be written as the flat space form plus subdominant correction terms dependent upon the geometric properties of the spacetime. This supports the use of flat space quantum inequalities to constrain negative energy effects in curved spacetime. Using the exact Euclidean two-point function method, we develop the quantum inequalities for perfectly reflecting planar mirrors in flat spacetime. We then look at the quantum inequalities in static de~Sitter spacetime, Rindler spacetime and two- and four-dimensional black holes. In the case of a four-dimensional Schwarzschild black hole, explicit forms of the inequality are found for static observers near the horizon and at large distances. It is show that there is a quantum averaged weak energy condition (QAWEC), which states that the energy density averaged over the entire worldline of a static observer is bounded below by the vacuum energy of the spacetime. In particular, for an observer at a fixed radial distance away from a black hole, the QAWEC says that the averaged energy density can never be less than the Boulware vacuum energy density.Comment: 27 pages, 2 Encapsulated Postscript figures, uses epsf.tex, typeset in RevTe

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

Possible evidence of a spontaneous spin-polarization in mesoscopic 2D electron systems

We have experimentally studied the non-equilibrium transport in low-density clean 2D electron systems at mesoscopic length scales. At zero magnetic field (B), a double-peak structure in the non-linear conductance was observed close to the Fermi energy in the localized regime. From the behavior of these peaks at non-zero B, we could associate them to the opposite spin states of the system, indicating a spontaneous spin polarization at B = 0. Detailed temperature and disorder dependence of the structure shows that such a splitting is a ground state property of the low-density 2D systems.Comment: 7 pages, 5 figure