Field Theoretical Quantum Effects on the Kerr Geometry

We study quantum aspects of the Einstein gravity with one time-like and one space-like Killing vector commuting with each other. The theory is formulated as a \coset nonlinear $\sigma$-model coupled to gravity. The quantum analysis of the nonlinear $\sigma$-model part, which includes all the dynamical degrees of freedom, can be carried out in a parallel way to ordinary nonlinear $\sigma$-models in spite of the existence of an unusual coupling. This means that we can investigate consistently the quantum properties of the Einstein gravity, though we are limited to the fluctuations depending only on two coordinates. We find the forms of the beta functions to all orders up to numerical coefficients. Finally we consider the quantum effects of the renormalization on the Kerr black hole as an example. It turns out that the asymptotically flat region remains intact and stable, while, in a certain approximation, it is shown that the inner geometry changes considerably however small the quantum effects may be.Comment: 16 pages, LaTeX. The hep-th number added on the cover, and minor typos correcte

Rotational Surfaces in L3\mathbb{L}^3 and Solutions in the Nonlinear Sigma Model

The Gauss map of non-degenerate surfaces in the three-dimensional Minkowski space are viewed as dynamical fields of the two-dimensional O(2,1) Nonlinear Sigma Model. In this setting, the moduli space of solutions with rotational symmetry is completely determined. Essentially, the solutions are warped products of orbits of the 1-dimensional groups of isometries and elastic curves in either a de Sitter plane, a hyperbolic plane or an anti de Sitter plane. The main tools are the equivalence of the two-dimensional O(2,1) Nonlinear Sigma Model and the Willmore problem, and the description of the surfaces with rotational symmetry. A complete classification of such surfaces is obtained in this paper. Indeed, a huge new family of Lorentzian rotational surfaces with a space-like axis is presented. The description of this new class of surfaces is based on a technique of surgery and a gluing process, which is illustrated by an algorithm.Comment: PACS: 11.10.Lm; 11.10.Ef; 11.15.-q; 11.30.-j; 02.30.-f; 02.40.-k. 45 pages, 11 figure

European Constitution and National Constitution

Preface "The history of the question of alliance, integration, and unification of European states along different lines reaches far back. We only have to mention I. Kant and J. C. Bluntschli, who saw the future of Europe in establishing a union of its states based on the rule of law. It was on the grounds of freedom and republican democracy that J. Lorimer of Edinburgh envisaged the possibility of uniting European states. Much like him, Polish thinkers too, including A. Mickiewicz, B. Limanowski, and K. Kelles-Krauz, believed that Europe would unite as soon as its constituent states were driven by shared ideals of freedom and republican democracy."(...

J. Gruszczak

this paper the test of smoothness is based (generally speaking) on verification of the following condition

Political and Legal Considerations Regarding the Negotiation of the Future UK-EU Security Relationship

In this chapter, the authors analyse potential transitional arrangements, discussing the possibilities of substantial delays in—or the no conclusion of—a security agreement, alternative models to the UK-EU relationship, dispute resolution and enforcement mechanisms in light of the UK Government’s red line on CJEU jurisdiction, and the UK’s potential reduced influence on future EU internal security