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