Extremal Isolated Horizons: A Local Uniqueness Theorem

We derive all the axi-symmetric, vacuum and electrovac extremal isolated horizons. It turns out that for every horizon in this class, the induced metric tensor, the rotation 1-form potential and the pullback of the electromagnetic field necessarily coincide with those induced by the monopolar, extremal Kerr-Newman solution on the event horizon. We also discuss the general case of a symmetric, extremal isolated horizon. In particular, we analyze the case of a two-dimensional symmetry group generated by two null vector fields. Its relevance to the classification of all the symmetric isolated horizons, including the non-extremal once, is explained.Comment: 22 pages, page size changed, typos and equations (142), (143a) corrected, PACS number adde

Geometry of Generic Isolated Horizons

Geometrical structures intrinsic to non-expanding, weakly isolated and isolated horizons are analyzed and compared with structures which arise in other contexts within general relativity, e.g., at null infinity. In particular, we address in detail the issue of singling out the preferred normals to these horizons required in various applications. This work provides powerful tools to extract invariant, physical information from numerical simulations of the near horizon, strong field geometry. While it complements the previous analysis of laws governing the mechanics of weakly isolated horizons, prior knowledge of those results is not assumed.Comment: 37 pages, REVTeX; Subsections V.B and V.C moved to a new Appenedix to improve the flow of main argument

Completeness of Wilson loop functionals on the moduli space of SL(2,C)SL(2,C) and SU(1,1)SU(1,1)-connections

The structure of the moduli spaces \M := \A/\G of (all, not just flat) $SL(2,C)$ and $SU(1,1)$ connections on a n-manifold is analysed. For any topology on the corresponding spaces \A of all connections which satisfies the weak requirement of compatibility with the affine structure of \A, the moduli space \M is shown to be non-Hausdorff. It is then shown that the Wilson loop functionals --i.e., the traces of holonomies of connections around closed loops-- are complete in the sense that they suffice to separate all separable points of \M. The methods are general enough to allow the underlying n-manifold to be topologically non-trivial and for connections to be defined on non-trivial bundles. The results have implications for canonical quantum general relativity in 4 and 3 dimensions.Comment: Plain TeX, 7 pages, SU-GP-93/4-

Two-loop RGE of a general renormalizable Yang-Mills theory in a renormalization scheme with an explicit UV cutoff

We perform a systematic one-loop renormalization of a general renormalizable Yang-Mills theory coupled to scalars and fermions using a regularization scheme with a smooth momentum cutoff $\Lambda$ (implemented through an exponential damping factor). We construct the necessary finite counterterms restoring the BRST invariance of the effective action by analyzing the relevant Slavnov-Taylor identities. We find the relation between the renormalized parameters in our scheme and in the conventional $\overline{\rm MS}$ scheme which allow us to obtain the explicit two-loop renormalization group equations in our scheme from the known two-loop ones in the $\overline{\rm MS}$ scheme. We calculate in our scheme the divergences of two-loop vacuum graphs in the presence of a constant scalar background field which allow us to rederive the two-loop beta functions for parameters of the scalar potential. We also prove that consistent application of the proposed regularization leads to counterterms which, together with the original action, combine to a bare action expressed in terms of bare parameters. This, together with treating $\Lambda$ as an intrinsic scale of a hypothetical underlying finite theory of all interactions, offers a possibility of an unconventional solution to the hierarchy problem if no intermediate scales between the electroweak scale and the Planck scale exist.Comment: updated references, 90 pages, many figure

Volume and Quantizations

The aim of this letter is to indicate the differences between the Rovelli-Smolin quantum volume operator and other quantum volume operators existing in the literature. The formulas for the operators are written in a unifying notation of the graph projective framework. It is clarified whose results apply to which operators and why.Comment: 8 page

Quantum group connections

The Ahtekar-Isham C*-algebra known from Loop Quantum Gravity is the algebra of continuous functions on the space of (generalized) connections with a compact structure Lie group. The algebra can be constructed by some inductive techniques from the C*-algebra of continuous functions on the group and a family of graphs embedded in the manifold underlying the connections. We generalize the latter construction replacing the commutative C*-algebra of continuous functions on the group by a non-commutative C*-algebra defining a compact quantum group.Comment: 40 pages, LaTeX2e, minor mistakes corrected, abstract slightly change

Issues in Model Validation

It is commonly agreed between modeling methodologists that model validation is one of the most important stages in the model building process. Many papers addressing this subject have been published and an SCS Technical Committee on Model Credibility has been established in order to generalize and summarize the experiences in this field (see Appendix) . However, at the present stage of research there are almost no suggestions concerning concrete methods of validation. Practically all authors only discuss definition of validation - not methods. The number of papers dealing with methods of model validation is also rather limited. The reason for this gap between methodological consciousness and the practice of model building seem to be obvious - the discussion stays at too high a level of abstraction. In general, all authors consider "model" as a description of reality, and on this level of concretization it is only possible to generate rather general statements, frequently true but without operational meaning. The author of this paper believes that, in order to examine validation methods, it is necessary to specify more precisely the model under consideration, the properties of the model, the modeling techniques, and, most importantly, the purpose of the model. The aim of this paper, therefore, is to present a classification of models and an analysis of the modeling process from the point of view of model validation. At this stage of the investigation, however, it is not yet possible to design, nor to analyze, methods of validation. Our goal is to design a framework for model validation as a first and important step in establishing a model validation methodology

Short Software Descriptions

This paper presents briefly the software for interactive decision support and software tools for developing decision support systems, developed in years 1985-1988 within the contracted study agreement between the System and Decision Sciences Program at IIASA and several Polish scientific institutions, including the following: Institute of Automatic Control, Warsaw University of Technology; Institute of Systems Research, Polish Academy of Sciences; Institute of Informatics, Warsaw University; Institute of Automatics, Academy of Mining and Metallurgy, Krakow. The theoretical part of the results developed within the project is presented in the IIASA Working Paper WP-88-071 entitled "Theory, Software and Testing Examples in Decision Support Systems". This volume contains also the theoretical and methodological backgrounds of the software systems developed within the project. These are presented shortly in this paper. Detailed software descriptions and user manuals have been published as separate IIASA Working Papers. Each Working Paper describes one software product and the title of such a paper corresponds to the title of the section in this paper. All software products in executable form are available to educational and scientific institutions, assuming that these products will not be used for commercial applications. Inquires for software should be directed to the System and Decision Sciences Program at IIASA, Methodology of Decision Analysis Project

SCDAS - Decision Support System for Group Decision Making: Information Processing Issues

Most research in the field of computerized Group Decision Support System is devoted to the analysis and support of the quantitative phase of decision processes using various methods of multiple-criteria analysis. Experience shows that the soft side of the decision process also needs support. This relates mostly to the distribution of textual information that augments the quantitative side of the decision process and to provides the linkage between such information and numerical data. This aspect is especially important when the decision support system is implemented in a distributed computing environment. In this paper possible forms of information processed within the SCDAS system are analyzed and the framework for implementing the software that provides such processing functions is presented