79 research outputs found
Black holes, cosmological singularities and change of signature
There exists a widespread belief that signature type change could be used to
avoid spacetime singularities. We show that signature change cannot be utilised
to this end unless the Einstein equation is abandoned at the suface of
signature type change. We also discuss how to solve the initial value problem
and show to which extent smooth and discontinuous signature changing solutions
are equivalent.Comment: 14pages, Latex, no figur
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
Initial Value Problems and Signature Change
We make a rigorous study of classical field equations on a 2-dimensional
signature changing spacetime using the techniques of operator theory. Boundary
conditions at the surface of signature change are determined by forming
self-adjoint extensions of the Schr\"odinger Hamiltonian. We show that the
initial value problem for the Klein--Gordon equation on this spacetime is
ill-posed in the sense that its solutions are unstable. Furthermore, if the
initial data is smooth and compactly supported away from the surface of
signature change, the solution has divergent -norm after finite time.Comment: 33 pages, LaTeX The introduction has been altered, and new work
(relating our previous results to continuous signature change) has been
include
Dimensionality, topology, energy, the cosmological constant, and signature change
Using the concept of real tunneling configurations (classical signature
change) and nucleation energy, we explore the consequences of an alternative
minimization procedure for the Euclidean action in multiple-dimensional quantum
cosmology. In both standard Hartle-Hawking type as well as Coleman type
wormhole-based approaches, it is suggested that the action should be minimized
among configurations of equal energy. In a simplified model, allowing for
arbitrary products of spheres as Euclidean solutions, the favoured space-time
dimension is 4, the global topology of spacelike slices being (hence predicting a universe of Kantowski-Sachs type). There is,
however, some freedom for a Kaluza-Klein scenario, in which case the observed
spacelike slices are . In this case, the internal space is a product
of two-spheres, and the total space-time dimension is 6, 8, 10 or 12.Comment: 34 pages, LaTeX, no figure
Comment on "Failure of standard conservation laws at a classical change of signature"
Hellaby & Dray (gr-qc/9404001) have recently claimed that matter conservation
fails under a change of signature, compounding earlier claims that the standard
junction conditions for signature change are unnecessary. In fact, if the field
equations are satisfied, then the junction conditions and the conservation
equations are satisfied. The failure is rather that the authors did not make
sense of the field equations and conservation equations, which are singular at
a change of signature.Comment: 3 pages, Te
Diffeomorphism algebra of two dimensional free massless scalar field with signature change
We study a model of free massless scalar fields on a two dimensional cylinder
with metric that admits a change of signature between Lorentzian and Euclidean
type (ET), across the two timelike hypersurfaces (with respect to Lorentzian
region). Considering a long strip-shaped region of the cylinder, denoted by an
angle \theta, as the signature changed region it is shown that the energy
spectrum depends on the angle \theta and in a sense differs from ordinary one
for low energies. Morever diffeomorphism algebra of corresponding infinite
conserved charges is different from '' Virasoro'' algebra and approaches to it
at higher energies. The central term is also modified but does not approach to
the ordinary one at higher energies.Comment: 18 pages, Latex, 2 ps figure
Signature change from Schutz's canonical quantum cosmology and its classical analogue
We study the signature change in a perfect fluid Friedmann-Robertson-Walker
quantum cosmological model. In this work the Schutz's variational formalism is
applied to recover the notion of time. This gives rise to a
Schrodinger-Wheeler-DeWitt equation with arbitrary ordering for the scale
factor. We use the eigenfunctions in order to construct wave packets and
evaluate the time-dependent expectation value of the scale factor which
coincides with the ontological interpretation. We show that these solutions
exhibit signature transitions from a finite Euclidean to a Lorentzian domain.
Moreover, such models are equivalent to a classical system where, besides the
perfect fluid, a repulsive fluid is present.Comment: 15 pages, 4 figures, to appear in PR
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
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
Zmiany regionalnych struktur sektora usług w krajach UE w latach 2010–2020
The development of the service sector, which is observed along with the increase in socio-economic development, is only one of the symptoms of changes in the economy. Much more important are the changes in the structure of the service sector itself. Due to the high heterogeneity of this sector, only a detailed analysis of changes to individual types of services gives a complete picture of the changes and the importance of the third sector in the economy.
The article’s main objective is to identify changes taking place in the structure of the EU countries’ services sector using the transfer method of share transfer. The analysis was carried out in the format of NACE sections (PKD) in 2010–2020 for the number of economic entities and employees in the territorial layout at the NUTS2 level.
The analysis concludes that there is a decline in the importance of traditional services under Section G, the development of professional, scientific and technical services (Section M) and an increase in the importance of ICT-related services (Section J). Polish regions do not differ from the panuropean pattern of change; some belonged to units with the most dynamically developing sections of the surveyed services in Europe.Rozwój sektora usług, który obserwowany jest wraz ze wzrostem poziomu rozwoju społeczno-gospodarczego, jest tylko jednym z symptomów przemian zachodzących w gospodarce. Znacznie istotniejsze są zmiany w strukturze samego sektora usług. Ze względu na dużą heterogeniczność tego sektora, dopiero analiza przekształceń w odniesieniu do poszczególnych rodzajów usług daje pełen obraz przemian i znaczenia trzeciego sektora w gospodarce.
Głównym celem artykułu jest identyfikacja zmian zachodzących w strukturze sektora usług krajów UE z wykorzystaniem metody przesunięć udziałów. Analiza została przeprowadzona w układzie sekcji NACE (PKD) w latach 2010–2020 dla liczby podmiotów gospodarczych oraz liczby zatrudnionych w układzie terytorialnym na poziomie NUTS2. Analiza prowadzi do wniosku, że następuje spadek znaczenia tradycyjnych usług zaliczanych do sekcji G oraz rozwój usług profesjonalnych, naukowych i technicznych (sekcja M), a także wzrost znaczenia usług związanych z sektorem ICT (sekcja J). Polskie regiony nie odstają od ogólnoeuropejskiego wzorca zmian, a niektóre z nich należały do jednostek z najdynamiczniej rozwijającymi się sekcjami badanych usług w Europie
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