1,365 research outputs found
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
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
Parametric Manifolds II: Intrinsic Approach
A parametric manifold is a manifold on which all tensor fields depend on an
additional parameter, such as time, together with a parametric structure,
namely a given (parametric) 1-form field. Such a manifold admits natural
generalizations of Lie differentiation, exterior differentiation, and covariant
differentiation, all based on a nonstandard action of vector fields on
functions. There is a new geometric object, called the deficiency, which
behaves much like torsion, and which measures whether a parametric manifold can
be viewed as a 1-parameter family of orthogonal hypersurfaces.Comment: Plain TeX, 13 pages, no figure
Failure of Standard Conservation Laws at a Classical Change of Signature
The Divergence Theorem as usually stated cannot be applied across a change of
signature unless it is re-expressed to allow for a finite source term on the
signature change surface. Consequently all conservation laws must also be
`modified', and therefore insistence on conservation of matter across such a
surface cannot be physically justified. The Darmois junction conditions
normally ensure conservation of matter via Israel's identities for the jump in
the energy-momentum density, but not when the signature changes. Modified
identities are derived for this jump when a signature change occurs, and the
resulting surface effects in the conservation laws are calculated. In general,
physical vector fields experience a jump in at least one component, and a
source term may therefore appear in the corresponding conservation law. Thus
current is also not conserved. These surface effects are a consequence of the
change in the character of physical law. The only way to recover standard
conservation laws is to impose restrictions that no realistic cosmological
model can satisfy.Comment: 15pp, figures available on request from Charles Hellaby at
[email protected]
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
The symplectic origin of conformal and Minkowski superspaces
Supermanifolds provide a very natural ground to understand and handle
supersymmetry from a geometric point of view; supersymmetry in and
dimensions is also deeply related to the normed division algebras.
In this paper we want to show the link between the conformal group and
certain types of symplectic transformations over division algebras. Inspired by
this observation we then propose a new\,realization of the real form of the 4
dimensional conformal and Minkowski superspaces we obtain, respectively, as a
Lagrangian supermanifold over the twistor superspace and a
big cell inside it.
The beauty of this approach is that it naturally generalizes to the 6
dimensional case (and possibly also to the 10 dimensional one) thus providing
an elegant and uniform characterization of the conformal superspaces.Comment: 15 pages, references added, minor change
Reply Comment: Comparison of Approaches to Classical Signature Change
We contrast the two approaches to ``classical" signature change used by
Hayward with the one used by us (Hellaby and Dray). There is (as yet) no
rigorous derivation of appropriate distributional field equations. Hayward's
distributional approach is based on a postulated modified form of the field
equations. We make an alternative postulate. We point out an important
difference between two possible philosophies of signature change --- ours is
strictly classical, while Hayward's Lagrangian approach adopts what amounts to
an imaginary proper ``time" on one side of the signature change, as is
explicitly done in quantum cosmology. We also explain why we chose to use the
Darmois-Israel type junction conditions, rather than the Lichnerowicz type
junction conditions favoured by Hayward. We show that the difference in results
is entirely explained by the difference in philosophy (imaginary versus real
Euclidean ``time"), and not by the difference in approach to junction
conditions (Lichnerowicz with specific coordinates versus Darmois with general
coordinates).Comment: 10 pages, latex, no figures. Replying to - "Comment on `Failure of
Standard Conservation Laws at a Classical Change of Signature'", S.A.
Hayward, Phys. Rev. D52, 7331-7332 (1995) (gr-qc/9606045
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
A New Look at the Ashtekar-Magnon Energy Condition
In 1975, Ashtekar and Magnon showed that an energy condition selects a unique
quantization procedure for certain observers in general, curved spacetimes. We
generalize this result in two important ways, by eliminating the need to assume
a particular form for the (quantum) Hamiltonian, and by considering the
surprisingly nontrivial extension to nonminimal coupling.Comment: REVTeX, 10 page
BOUNDARY CONDITIONS FOR THE SCALAR FIELD IN THE PRESENCE OF SIGNATURE CHANGE
We show that, contrary to recent criticism, our previous work yields a
reasonable class of solutions for the massless scalar field in the presence of
signature change.Comment: 11 pages, Plain Tex, no figure
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