1,421 research outputs found
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 ,\dots 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 . 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 â known as the âProtocol of Canberraâ â 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
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