Averaged Energy Conditions and Evaporating Black Holes

In this paper the averaged weak (AWEC) and averaged null (ANEC) energy conditions, together with uncertainty principle-type restrictions on negative energy (``quantum inequalities''), are examined in the context of evaporating black hole backgrounds in both two and four dimensions. In particular, integrals over only half-geodesics are studied. We determine the regions of the spacetime in which the averaged energy conditions are violated. In all cases where these conditions fail, there appear to be quantum inequalities which bound the magnitude and extent of the negative energy, and hence the degree of the violation. The possible relevance of these results for the validity of singularity theorems in evaporating black hole spacetimes is discussed.Comment: Sections 2.1 and 2.2 have been revised and some erroneous statements corrected. The main conclusions and the figures are unchanged. 27 pp, plain Latex, 3 figures available upon reques

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

Modelling and control of a high redundancy actuator

The high redundancy actuation concept is a completely new approach to fault tolerance, and it is important to appreciate that it provides a transformation of the characteristics of actuators so that the actuation performance (capability) degrades slowly rather than suddenly failing, even though individual elements themselves fail. This paper aims to demonstrate the viability of the concept by showing that a highly redundant actuator, comprising a relatively large number of actuation elements, can be controlled in such a way that faults in individual elements are inherently accommodated, although some degradation in overall performance will inevitably be found. The paper introduces the notion of fault-tolerant systems and the highly redundant actuator concept. Then a model for a two by two configuration with electro-mechanical actuation elements is derived. Two classical control approaches are then considered based on frequency domain techniques. Finally simulation results under a number of faults show the viability of the approach for fault accommodation without re-configuratio

Radiative corrections to the Casimir effect for the massive scalar field

We compute the $O(\lambda)$ correction to the Casimir energy for the massive $\lambda\phi^4$ model confined between a pair of parallel plates. The calculations are made with Dirichlet and Neumann boundary conditions. The correction is shown to be sensitive to the boundary conditions, except in the zero mass limit, in which case our results agree with those found in the literature.Comment: 6 pages. Work presented at the XXIII Brazilian National Meeting on Particles and Fields (Aguas de Lindoia, Brazil, 15-19 Oct 2002). Also available at http://www.sbf1.if.usp.br/eventos/enfpc/xxiii/procs/RES142.pd

Focusing and the Holographic Hypothesis

The ``screen mapping" introduced by Susskind to implement 't Hooft's holographic hypothesis is studied. For a single screen time, there are an infinite number of images of a black hole event horizon, almost all of which have smaller area on the screen than the horizon area. This is consistent with the focusing equation because of the existence of focal points. However, the {\it boundary} of the past (or future) of the screen obeys the area theorem, and so always gives an expanding map to the screen, as required by the holographic hypothesis. These considerations are illustrated with several axisymmetric static black hole spacetimes.Comment: 8 pages, plain latex, 5 figures included using psfi

Non-Coexistence of Infinite Clusters in Two-Dimensional Dependent Site Percolation

This paper presents three results on dependent site percolation on the square lattice. First, there exists no positively associated probability measure on {0,1}^{Z^2} with the following properties: a) a single infinite 0cluster exists almost surely, b) at most one infinite 1*cluster exists almost surely, c) some probabilities regarding 1*clusters are bounded away from zero. Second, we show that coexistence of an infinite 1*cluster and an infinite 0cluster is almost surely impossible when the underlying probability measure is ergodic with respect to translations, positively associated, and satisfies the finite energy condition. The third result analyses the typical structure of infinite clusters of both types in the absence of positive association. Namely, under a slightly sharpened finite energy condition, the existence of infinitely many disjoint infinite self-avoiding 1*paths follows from the existence of an infinite 1*cluster. The same holds with respect to 0paths and 0clusters.Comment: 17 pages, 1 figur

The Effect of Negative-Energy Shells on the Schwarzschild Black Hole

We construct Penrose diagrams for Schwarzschild spacetimes joined by massless shells of matter, in the process correcting minor flaws in the similar diagrams drawn by Dray and 't Hooft, and confirming their result that such shells generate a horizon shift. We then consider shells with negative energy density, showing that the horizon shift in this case allows for travel between the heretofore causally separated exterior regions of the Schwarzschild geometry. These drawing techniques are then used to investigate the properties of successive shells, joining multiple Schwarzschild regions. Again, the presence of negative-energy shells leads to a causal connection between the exterior regions, even in (some) cases with two successive shells of equal but opposite total energy.Comment: 12 pages, 10 figure

The Dirichlet Casimir effect for ϕ4\phi^4 theory in (3+1) dimensions: A new renormalization approach

We calculate the next to the leading order Casimir effect for a real scalar field, within $\phi^4$ theory, confined between two parallel plates in three spatial dimensions with the Dirichlet boundary condition. In this paper we introduce a systematic perturbation expansion in which the counterterms automatically turn out to be consistent with the boundary conditions. This will inevitably lead to nontrivial position dependence for physical quantities, as a manifestation of the breaking of the translational invariance. This is in contrast to the usual usage of the counterterms in problems with nontrivial boundary conditions, which are either completely derived from the free cases or at most supplemented with the addition of counterterms only at the boundaries. Our results for the massive and massless cases are different from those reported elsewhere. Secondly, and probably less importantly, we use a supplementary renormalization procedure, which makes the usage of any analytic continuation techniques unnecessary.Comment: JHEP3 format,20 pages, 2 figures, to appear in JHE

Fluctuations of an evaporating black hole from back reaction of its Hawking radiation: Questioning a premise in earlier work

This paper delineates the first steps in a systematic quantitative study of the spacetime fluctuations induced by quantum fields in an evaporating black hole. We explain how the stochastic gravity formalism can be a useful tool for that purpose within a low-energy effective field theory approach to quantum gravity. As an explicit example we apply it to the study of the spherically-symmetric sector of metric perturbations around an evaporating black hole background geometry. For macroscopic black holes we find that those fluctuations grow and eventually become important when considering sufficiently long periods of time (of the order of the evaporation time), but well before the Planckian regime is reached. In addition, the assumption of a simple correlation between the fluctuations of the energy flux crossing the horizon and far from it, which was made in earlier work on spherically-symmetric induced fluctuations, is carefully analyzed and found to be invalid. Our analysis suggests the existence of an infinite amplitude for the fluctuations of the horizon as a three-dimensional hypersurface. We emphasize the need for understanding and designing operational ways of probing quantum metric fluctuations near the horizon and extracting physically meaningful information.Comment: 10 pages, REVTeX; minor changes, a few references added and a brief discussion of their relevance included. To appear in the proceedings of the 10th Peyresq meeting. Dedicated to Rafael Sorkin on the occasion of his 60th birthda