Inflationary spacetimes are not past-complete

Many inflating spacetimes are likely to violate the weak energy condition, a key assumption of singularity theorems. Here we offer a simple kinematical argument, requiring no energy condition, that a cosmological model which is inflating -- or just expanding sufficiently fast -- must be incomplete in null and timelike past directions. Specifically, we obtain a bound on the integral of the Hubble parameter over a past-directed timelike or null geodesic. Thus inflationary models require physics other than inflation to describe the past boundary of the inflating region of spacetime.Comment: We improve the basic argument to apply to a wider class of spacetimes, use a better title and add a discussion of cyclic models. 4 pages, 1 figure, RevTe

High-contrast Imaging from Space: Speckle Nulling in a Low Aberration Regime

High-contrast imaging from space must overcome two major noise sources to successfully detect a terrestrial planet angularly close to its parent star: photon noise from diffracted star light, and speckle noise from star light scattered by instrumentally-generated wavefront perturbation. Coronagraphs tackle only the photon noise contribution by reducing diffracted star light at the location of a planet. Speckle noise should be addressed with adaptative-optics systems. Following the tracks of Malbet, Yu and Shao (1995), we develop in this paper two analytical methods for wavefront sensing and control that aims at creating dark holes, i.e. areas of the image plane cleared out of speckles, assuming an ideal coronagraph and small aberrations. The first method, speckle field nulling, is a fast FFT-based algorithm that requires the deformable-mirror influence functions to have identical shapes. The second method, speckle energy minimization, is more general and provides the optimal deformable mirror shape via matrix inversion. With a NxN deformable mirror, the size of matrix to be inverted is either N^2xN^2 in the general case, or only NxN if influence functions can be written as the tensor product of two one-dimensional functions. Moreover, speckle energy minimization makes it possible to trade off some of the dark hole area against an improved contrast. For both methods, complex wavefront aberrations (amplitude and phase) are measured using just three images taken with the science camera (no dedicated wavefront sensing channel is used), therefore there are no non-common path errors. We assess the theoretical performance of both methods with numerical simulations, and find that these speckle nulling techniques should be able to improve the contrast by several orders of magnitude.Comment: 31 pages, 8 figures, 1 table. Accepted for publication in ApJ (should appear in February 2006

Violations of the Weak Energy Condition in Inflating Spacetimes

We argue that many future-eternal inflating spacetimes are likely to violate the weak energy condition. It is possible that such spacetimes may not enforce any of the known averaged conditions either. If this is indeed the case, it may open the door to constructing non-singular, past-eternal inflating cosmologies. Simple non-singular models are, however, unsatisfactory, and it is not clear if satisfactory models can be built that solve the problem of the initial singularity.Comment: 18 pages, 1 figure (which emerges automatically if you use dvips

Non-Singular Charged Black Hole Solution for Non-Linear Source

A non-singular exact black hole solution in General Relativity is presented. The source is a non-linear electromagnetic field, which reduces to the Maxwell theory for weak field. The solution corresponds to a charged black hole with |q| \leq 2s_c m \approx 0.6 m, having metric, curvature invariants, and electric field bounded everywhere.Comment: 3 pages, RevTe

Risks to Hospitality Firms in the International Arena

Much potential for growth in hospitality firms exists in foreign countries, but expansion abroad typicality bears additional risks that could be detrimental to the operations. The authors explore those risks, currency exchange risk, and country risk, and offer practical techniques to access, manage, control, and reduce them. Deriving benefits from global opportunities requires effective management of these area

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.

Curing singularities: From the big bang to black holes

Singular spacetimes are a natural prediction of Einstein's theory. Most memorable are the singular centers of black holes and the big bang. However, dilatonic extensions of Einstein's theory can support nonsingular spacetimes. The cosmological singularities can be avoided by dilaton driven inflation. Furthermore, a nonsingular black hole can be constructed in two dimensions.Comment: To appear as a brief report in Phys. Rev.

Open and Closed Universes, Initial Singularities and Inflation

The existence of initial singularities in expanding universes is proved without assuming the timelike convergence condition. The assumptions made in the proof are ones likely to hold both in open universes and in many closed ones. (It is further argued that at least some of the expanding closed universes that do not obey a key assumption of the theorem will have initial singularities on other grounds.) The result is significant for two reasons: (a)~previous closed-universe singularity theorems have assumed the timelike convergence condition, and (b)~the timelike convergence condition is known to be violated in inflationary spacetimes. An immediate consequence of this theorem is that a recent result on initial singularities in open, future-eternal, inflating spacetimes may now be extended to include many closed universes. Also, as a fringe benefit, the time-reverse of the theorem may be applied to gravitational collapse.Comment: 27 pages, Plain TeX (figures are embedded in the file itself and they will emerge if it is processed according to the instructions at the top of the file

On T-Duality in Brane Gas Cosmology

In the context of homogeneous and isotropic superstring cosmology, the T-duality symmetry of string theory has been used to argue that for a background space-time described by dilaton gravity with strings as matter sources, the cosmological evolution of the Universe will be nonsingular. In this Letter we discuss how T-duality extends to brane gas cosmology, an approximation in which the background space-time is again described by dilaton gravity with a gas of branes as a matter source. We conclude that the arguments for nonsingular cosmological evolution remain valid.Comment: 8 pages, Appendix adde