76 research outputs found
Volksbegehren und Volksentscheid
Auf Landes- und Kommunalebene sind Volksbegehren und Volksentscheid inzwischen in allen 16 Ländern eröffnet. Die vorherigen Warnungen der Gegner haben sich als unberechtigt erwiesen. Es ist an der Zeit, Direkte Demokratie auch auf Bundesebene einzuführen. ..
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
Cosmological perturbations and classical change of signature
Cosmological perturbations on a manifold admitting signature change are
studied. The background solution consists in a Friedmann-Lemaitre-Robertson-
Walker (FLRW) Universe filled by a constant scalar field playing the role of a
cosmological constant. It is shown that no regular solution exist satisfying
the junction conditions at the surface of change. The comparison with similar
studies in quantum cosmology is made.Comment: 35 pages, latex, 2 figures available at [email protected], to
appear in Physical Review
General solutions of Einstein's spherically symmetric gravitational equations with junction conditions
Einstein's spherically symmetric interior gravitational equations are
investigated. Following Synge's procedure, the most general solution of the
equations is furnished in case and are prescribed. The
existence of a total mass function, , is rigorously proved. Under
suitable restrictions on the total mass function, the Schwarzschild mass
, implicitly defines the boundary of the spherical body as .
Both Synge's junction conditions as well as the continuity of the second
fundamental form are examined and solved in a general manner. The weak energy
conditions for an \emph{arbitrary boost} are also considered. The most general
solution of the spherically symmetric anisotropic fluid model satisfying both
junction conditions is furnished. In the final section, various exotic
solutions are explored using the developed scheme including gravitational
instantons, interior -domains and -dimensional generalizations.Comment: 23 pages, 1 figure, uses AMS packages. Updated version has corrected
typos as well as added comments and extension regarding ISLD junction
conditions. Accepted for publication in Journal of Mathematical Physic
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
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