Piecewise Conserved Quantities

We review the treatment of conservation laws in spacetimes that are glued together in various ways, thus adding a boundary term to the usual conservation laws. Several examples of such spacetimes will be described, including the joining of Schwarzschild spacetimes of different masses, and the possibility of joining regions of different signatures. The opportunity will also be taken to explore some of the less obvious properties of Lorentzian vector calculus.Comment: To appear in Gravity and the Quantum, Springer 2017 (http://www.springer.com/in/book/9783319516998

Note on Signature Change and Colombeau Theory

Recent work alludes to various `controversies' associated with signature change in general relativity. As we have argued previously, these are in fact disagreements about the (often unstated) assumptions underlying various possible approaches. The choice between approaches remains open.Comment: REVTex, 3 pages; to appear in GR

Gravity and Signature Change

The use of proper ``time'' to describe classical ``spacetimes'' which contain both Euclidean and Lorentzian regions permits the introduction of smooth (generalized) orthonormal frames. This remarkable fact permits one to describe both a variational treatment of Einstein's equations and distribution theory using straightforward generalizations of the standard treatments for constant signature.Comment: Plain TeX, 6 pages; to appear in GR

Chemical Self-Enrichment of HII Regions by the Wolf-Rayet Phase of an 85 Msun star

It is clear from stellar evolution and from observations of WR stars that massive stars are releasing metal-enriched gas through their stellar winds in the Wolf-Rayet phase. Although HII region spectra serve as diagnostics to determine the present-day chemical composition of the interstellar medium, it is far from being understood to what extent the HII gas is already contaminated by chemically processed stellar wind. Therefore, we analyzed our models of radiative and wind bubbles of an isolated 85 Msun star with solar metallicity (Kr\"oger et al. 2006) with respect to the chemical enrichment of the circumstellar HII region. Plausibly, the hot stellar wind bubble (SWB) is enriched with 14N during the WN phase and even much higher with 12C and 16O during the WC phase of the star. During the short period that the 85 Msun star spends in the WC stage enriched SWB material mixes with warm HII gas of solar abundances and thus enhances the metallicity in the HII region. However, at the end of the stellar lifetime the mass ratios of the traced elements N and O in the warm ionized gas are insignificantly higher than solar, whereas an enrichment of 22 % above solar is found for C. Important issues from the presented study comprise a steeper radial gradient of C than O and a decreasing effect of self-enrichment for metal-poor galaxies.Comment: 5 pages, 3 figures, accepted for publication in A&A Letter

Comment on `Smooth and Discontinuous Signature Type Change in General Relativity'

Kossowski and Kriele derived boundary conditions on the metric at a surface of signature change. We point out that their derivation is based not only on certain smoothness assumptions but also on a postulated form of the Einstein field equations. Since there is no canonical form of the field equations at a change of signature, their conclusions are not inescapable. We show here that a weaker formulation is possible, in which less restrictive smoothness assumptions are made, and (a slightly different form of) the Einstein field equations are satisfied. In particular, in this formulation it is possible to have a bounded energy-momentum tensor at a change of signature without satisfying their condition that the extrinsic curvature vanish.Comment: Plain TeX, 6 pages; Comment on Kossowski and Kriele: Class. Quantum Grav. 10, 2363 (1993); Reply by Kriele: Gen. Rel. Grav. 28, 1409-1413 (1996

Actions for signature change

This is a contribution on the controversy about junction conditions for classical signature change. The central issue in this debate is whether the extrinsic curvature on slices near the hypersurface of signature change has to be continuous ({\it weak} signature change) or to vanish ({\it strong} signature change). Led by a Lagrangian point of view, we write down eight candidate action functionals $S_1$,\dots $S_8$ as possible generalizations of general relativity and investigate to what extent each of these defines a sensible variational problem, and which junction condition is implied. Four of the actions involve an integration over the total manifold. A particular subtlety arises from the precise definition of the Einstein-Hilbert Lagrangian density $|g|^{1/2} R[g]$. The other four actions are constructed as sums of integrals over singe-signature domains. The result is that {\it both} types of junction conditions occur in different models, i.e. are based on different first principles, none of which can be claimed to represent the ''correct'' one, unless physical predictions are taken into account. From a point of view of naturality dictated by the variational formalism, {\it weak} signature change is slightly favoured over {\it strong} one, because it requires less {\it \`a priori} restrictions for the class of off-shell metrics. In addition, a proposal for the use of the Lagrangian framework in cosmology is made.Comment: 36 pages, LaTeX, no figures; some corrections have been made, several Comments and further references are included and a note has been added

Black holes from high-energy beam--beam collisions

Using a recent technique, proposed by Eardley and Giddings, we extend their results to the high-energy collision of two beams of massless particles, i.e. of two finite-front shock waves. Closed (marginally) trapped surfaces can be determined analytically in several cases even for collisions at non-vanishing impact parameter in D\ge 4 space-time dimensions. We are able to confirm and extend earlier conjectures by Yurtsever, and to deal with arbitrary axisymmetric profiles, including an amusing case of ``fractal'' beams. We finally discuss some implications of our results in high-energy experiments and in cosmology.Comment: 17 pages Revtex, 1 figure, references adde

Stochastic Tachyon Fluctuations, Marginal Deformations and Shock Waves in String Theory

Starting with exact solutions to string theory on curved spacetimes we obtain deformations that represent gravitational shock waves. These may exist in the presence or absence of sources. Sources are effectively induced by a tachyon field that randomly fluctuates around a zero condensate value. It is shown that at the level of the underlying conformal field theory (CFT) these deformations are marginal and moreover all \a'-corrections are taken into account. Explicit results are given when the original undeformed 4-dimensional backgrounds correspond to tensor products of combinations of 2-dimensional CFT's, for instance SL(2,R)/R \times SU(2)/U(1).Comment: 26 pages, harvmac, no figures. Very minor modifications, and in addition conditions (B.3) and (B.4) were also obtained using beta-function equations. Version to appear in Phys. Rev.

Evaluating Participatory Modeling: Developing a Framework for Cross-case Analysis

Participatory modeling is increasingly recognised as an effective way to assist collective decision-making processes in the domain of natural resource management. This paper introduces a framework for evaluating projects that have adopted a participatory modeling approach. This framework – known as the ‘Protocol of Canberra’ – was developed through a collaboration between French and Australian researchers engaged in participatory modeling and evaluation research. The framework seeks to assess the extent to which different participatory modeling practices reinforce or divert from the theoretical assumptions they are built upon. The paper discusses the application of the framework in three case-studies, two from Australia and one from the Pacific island of the Republic of Kiribati. The paper concludes with some comments for future use of the framework in a range of participatory modeling contexts, including fostering consideration of why and how different methodological approaches are used to achieve project aims and to build a collective vision amongst diverse stakeholders.participation, modeling, evaluation, complex systems science

The trace left by signature-change-induced compactification

Recently, it has been shown that an infinite succession of classical signature changes (''signature oscillations'') can compactify and stabilize internal dimensions, and simultaneously leads, after a coarse graining type of average procedure, to an effective (''physical'') space-time geometry displaying the usual Lorentzian metric signature. Here, we consider a minimally coupled scalar field on such an oscillating background and study its effective dynamics. It turns out that the resulting field equation in four dimensions contains a coupling to some non-metric structure, the imprint of the ''microscopic'' signature oscillations on the effective properties of matter. In a multidimensional FRW model, this structure is identical to a massive scalar field evolving in its homogeneous mode.Comment: 15 pages, LaTeX, no figure