Determination and Reduction of Large Diffeomorphisms

Within the Hamiltonian formulation of diffeomorphism invariant theories we address the problem of how to determine and how to reduce diffeomorphisms outside the identity component.Comment: 4 pages, Latex, macro espcrc2.sty. Contribution to the proceedings of the second conference on Constrained Dynamics and Quantum Gravity, Santa Margherita, Italy, 17-21 September 1996. To appear in Nucl. Phys. B Supp

Quantum Mechanics On Spaces With Finite Fundamental Group

We consider in general terms dynamical systems with finite-dimensional, non-simply connected configuration-spaces. The fundamental group is assumed to be finite. We analyze in full detail those ambiguities in the quantization procedure that arise from the non-simply connectedness of the classical configuration space. We define the quantum theory on the universal cover but restrict the algebra of observables \O to the commutant of the algebra generated by deck-transformations. We apply standard superselection principles and construct the corresponding sectors. We emphasize the relevance of all sectors and not just the abelian ones.Comment: 40 Pages, Plain-TeX, no figure

Group Averaging and Refined Algebraic Quantization

We review the framework of Refined Algebraic Quantization and the method of Group Averaging for quantizing systems with first-class constraints. Aspects and results concerning the generality, limitations, and uniqueness of these methods are discussed.Comment: 4 pages, LaTeX 2.09 using espcrc2.sty. To appear in the proceedings of the third "Meeting on Constrained Dynamics and Quantum Gravity", Nucl. Phys. B (Proc. Suppl.

Asymptotic Symmetry Groups of Long-Ranged Gauge Configurations

We make some general remarks on long-ranged configurations in gauge or diffeomorphism invariant theories where the fields are allowed to assume some non vanishing values at spatial infinity. In this case the Gauss constraint only eliminates those gauge degrees of freedom which lie in the connected component of asymptotically trivial gauge transformations. This implies that proper physical symmetries arise either from gauge transformations that reach to infinity or those that are asymptotically trivial but do not lie in the connected component of transformations within that class. The latter transformations form a discrete subgroup of all symmetries whose position in the ambient group has proven to have interesting implications. We explain this for the dyon configuration in the $SO(3)$ Yang-Mills-Higgs theory, where we prove that the asymptotic symmetry group is $Z_{|m|}\times \Re$ where $m$ is the monopole number. We also discuss the application of the general setting to general relativity and show that here the only implication of discrete symmetries for the continuous part is a possible extension of the rotation group $SO(3)$ to $SU(2)$.Comment: 14 pages, Plain TeX, Report CGPG-94/10-

On the Construction of Time-Symmetric Black Hole Initial Data

We review in a pedagogical fashion the 3+1-split which serves to put Einstein's equations into the form of a dynamical system with constraints. We then discuss the constraint equations under the simplifying assumption of time-symmetry. Multi-Black-Hole data are presented and more explicitly described in the case of two holes. The effect of different topologies is emphasized.Comment: 18 pages, Latex, uses Springer style-file lamuphys.sty. To appear in "Black Holes: Theory and Observation", edited by F. Hehl, C. Kiefer and R. Metzler, Springer 199

The Generalized Thin-Sandwich Problem and its Local Solvability

We consider Einstein Gravity coupled to dynamical matter consisting of a gauge field with any compact gauge group and minimally coupled scalar fields. We investigate the conditions under which a free specification of a spatial field configuration for the total system and its derivative with respect to coordinate-time determines a solution to the field equations (generalized thin-sandwich problem). Sufficient conditions for local solvability (in the space of fields) are established.Comment: 18 pages, Plain Te

Is There a General Area Theorem for Black Holes?

The general validity of the area law for black holes is still an open problem. We first show in detail how to complete the usually incompletely stated text-book proofs under the assumption of piecewise $C^2$-smoothness for the surface of the black hole. Then we prove that a black hole surface necessarily contains points where it is not $C^1$ (called ``cusps'') at any time before caustics of the horizon generators show up, like e.g. in merging processes. This implies that caustics never disappear in the past and that black holes without initial cusps will never develop such. Hence black holes which will undergo any non-trivial processes anywhere in the future will always show cusps. Although this does not yet imply a strict incompatibility with piecewise $C^2$ structures, it indicates that the latter are likely to be physically unnatural. We conclude by calling for a purely measure-theoretic proof of the area theorem.Comment: 7 pages, TeX; the proof for existence of cusps is generalized, new material and references include