1,471 research outputs found
Classical and Quantum Gravity in 1+1 Dimensions, Part II: The Universal Coverings
A set of simple rules for constructing the maximal (e.g. analytic) extensions
for any metric with a Killing field in an (effectively) two-dimensional
spacetime is formulated. The application of these rules is extremely
straightforward, as is demonstrated at various examples and illustrated with
numerous figures. Despite the resulting simplicity we also comment on some
subtleties concerning the concept of Penrose diagrams. Most noteworthy among
these, maybe, is that (smooth) spacetimes which have both degenerate and
non-degenerate (Killing) horizons do not allow for globally smooth Penrose
diagrams. Physically speaking this obstruction corresponds to an infinite
relative red/blueshift between observers moving across the two horizons. -- The
present work provides a further step in the classification of all global
solutions of the general class of two-dimensional gravity-Yang-Mills systems
introduced in Part I, comprising, e.g., all generalized (linear and nonlinear)
dilaton theories. In Part I we constructed the local solutions, which were
found to always have a Killing field; in this paper we provide all universal
covering solutions (the simply connected maximally extended spacetimes). A
subsequent Part III will treat the diffeomorphism inequivalent solutions for
all other spacetime topologies. -- Part II is kept entirely self-contained; a
prior reading of Part I is not necessary.Comment: 29 pages, 14 Postscript figures; one figure, some paragraphs, and
references added; to appear in Class. Quantum Gra
Lie Algebroid Yang Mills with Matter Fields
Lie algebroid Yang-Mills theories are a generalization of Yang-Mills gauge
theories, replacing the structural Lie algebra by a Lie algebroid E. In this
note we relax the conditions on the fiber metric of E for gauge invariance of
the action functional. Coupling to scalar fields requires possibly nonlinear
representations of Lie algebroids. In all cases, gauge invariance is seen to
lead to a condition of covariant constancy on the respective fiber metric in
question with respect to an appropriate Lie algebroid connection.
The presentation is kept in part explicit so as to be accessible also to a
less mathematically oriented audience.Comment: 24 pages, accepted for publication in J. Geom. Phy
2d quantum dilaton gravity as/versus finite dimensional quantum mechanical systems
I present the ``Chern--Simons'' formulation of generalized 2d dilaton
gravity, summarize its Hamiltonian quantization (reduced phase space and Dirac
quantization) and briefly discuss the statistical mechanical entropy of 2d
black holes. Focus is put on the close relation to finite dimensional point
particle systems.Comment: 4 pages, Latex; talk delivered at the 2nd Conference on Constrained
Dynamics and Quantum Gravity, Santa Margherita Ligure, September 199
Explicit Global Coordinates for Schwarzschild and Reissner-Nordstroem
We construct coordinate systems that cover all of the Reissner-Nordstroem
solution with m>|q| and m=|q|, respectively. This is possible by means of
elementary analytical functions. The limit of vanishing charge q provides an
alternative to Kruskal which, to our mind, is more explicit and simpler. The
main tool for finding these global charts is the description of highly
symmetrical metrics by two-dimensional actions. Careful gauge fixing yields
global representatives of the two-dimensional theory that can be rewritten
easily as the corresponding four-dimensional line elements.Comment: 12 pages, 3 Postscript figures, sign error in Eq. (37) and below
corrected, references and Note added; to appear in Class. Quantum Gra
WZW-Poisson manifolds
We observe that a term of the WZW-type can be added to the Lagrangian of the
Poisson Sigma model in such a way that the algebra of the first class
constraints remains closed. This leads to a natural generalization of the
concept of Poisson geometry. The resulting "WZW-Poisson" manifold M is
characterized by a bivector Pi and by a closed three-form H such that
[Pi,Pi]_Schouten = .Comment: 4 pages; v2: a reference adde
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