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

General polarization modes for the Rosen gravitational wave

Strong-field gravitational plane waves are often represented in either the Rosen or Brinkmann forms. While these two metric ansatze are related by a coordinate transformation, so that they should describe essentially the same physics, they rather puzzlingly seem to treat polarization states quite differently. Both ansatze deal equally well with + and X linear polarizations, but there is a qualitative difference in they way they deal with circular, elliptic, and more general polarization states. In this article we will develop a general formalism for dealing with arbitrary polarization states in the Rosen form of the gravitational wave metric, representing an arbitrary polarization by a trajectory in a suitably defined two dimensional hyperbolic plane.Comment: V1: 12 pages, no figures. V2: still 12 pages, reformatted. Minor technical edits, discussion of Riemann tensor added, two references added, no significant physics changes. This version accepted for publication in Classical and Quantum Gravit

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.

Cosmodynamics: Energy conditions, Hubble bounds, density bounds, time and distance bounds

We refine and extend a programme initiated by one of the current authors [Science 276 (1997) 88; Phys. Rev. D56 (1997) 7578] advocating the use of the classical energy conditions of general relativity in a cosmological setting to place very general bounds on various cosmological parameters. We show how the energy conditions can be used to bound the Hubble parameter H(z), Omega parameter Omega(z), density rho(z), distance d(z), and lookback time T(z) as (relatively) simple functions of the redshift z, present-epoch Hubble parameter H_0, and present-epoch Omega parameter Omega_0. We compare these results with related observations in the literature, and confront the bounds with the recent supernova data.Comment: 21 pages, 2 figure

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

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

Assessing the Viability of Complex Electrical Impedance Tomography (EIT) with a Spatially Distributed Sensor Array for Imaging of River Bed Morphology: a Proof of Concept (Study)

This report was produced as part of a NERC funded ‘Connect A’ project to establish a new collaborative partnership between the University of Worcester (UW) and Q-par Angus Ltd. The project aim was to assess the potential of using complex Electrical Impedance Tomography (EIT) to image river bed morphology. An assessment of the viability of sensors inserted vertically into the channel margins to provide real-time or near real-time monitoring of bed morphology is reported. Funding has enabled UW to carry out a literature review of the use of EIT and existing methods used for river bed surveys, and outline the requirements of potential end-users. Q-par Angus has led technical developments and assessed the viability of EIT for this purpose. EIT is one of a suite of tomographic imaging techniques and has already been used as an imaging tool for medical analysis, industrial processing and geophysical site survey work. The method uses electrodes placed on the margins or boundary of the entity being imaged, and a current is applied to some and measured on the remaining ones. Tomographic reconstruction uses algorithms to estimate the distribution of conductivity within the object and produce an image of this distribution from impedance measurements. The advantages of the use of EIT lie with the inherent simplicity, low cost and portability of the hardware, the high speed of data acquisition for real-time or near real-time monitoring, robust sensors, and the object being monitored is done so in a non-invasive manner. The need for sophisticated image reconstruction algorithms, and providing images with adequate spatial resolution are key challenges. A literature review of the use of EIT suggests that to date, despite its many other applications, to the best of our knowledge only one study has utilised EIT for river survey work (Sambuelli et al 2002). The Sambuelli (2002) study supported the notion that EIT may provide an innovative way of describing river bed morphology in a cost effective way. However this study used an invasive sensor array, and therefore the potential for using EIT in a non-invasive way in a river environment is still to be tested. A review of existing methods to monitor river bed morphology indicates that a plethora of techniques have been applied by a range of disciplines including fluvial geomorphology, ecology and engineering. However, none provide non-invasive, low costs assessments in real-time or near real-time. Therefore, EIT has the potential to meet the requirements of end users that no existing technique can accomplish. Work led by Q-par Angus Ltd. has assessed the technical requirements of the proposed approach, including probe design and deployment, sensor array parameters, data acquisition, image reconstruction and test procedure. Consequently, the success of this collaboration, literature review, identification of the proposed approach and potential applications of this technique have encouraged the authors to seek further funding to test, develop and market this approach through the development of a new environmental sensor

Gravitational vacuum polarization IV: Energy conditions in the Unruh vacuum

Building on a series of earlier papers [gr-qc/9604007, gr-qc/9604008, gr-qc/9604009], I investigate the various point-wise and averaged energy conditions in the Unruh vacuum. I consider the quantum stress-energy tensor corresponding to a conformally coupled massless scalar field, work in the test-field limit, restrict attention to the Schwarzschild geometry, and invoke a mixture of analytical and numerical techniques. I construct a semi-analytic model for the stress-energy tensor that globally reproduces all known numerical results to within 0.8%, and satisfies all known analytic features of the stress-energy tensor. I show that in the Unruh vacuum (1) all standard point-wise energy conditions are violated throughout the exterior region--all the way from spatial infinity down to the event horizon, and (2) the averaged null energy condition is violated on all outgoing radial null geodesics. In a pair of appendices I indicate general strategy for constructing semi-analytic models for the stress-energy tensor in the Hartle-Hawking and Boulware states, and show that the Page approximation is in a certain sense the minimal ansatz compatible with general properties of the stress-energy in the Hartle-Hawking state.Comment: 40 pages; plain LaTeX; uses epsf.sty (ten encapsulated postscript figures); two tables (table and tabular environments). Should successfully compile under both LaTeX 209 and the 209 compatibility mode of LaTeX2