Jakub Mielczarek (Cracow)

Signature change in loop quantum cosmology

The Wick rotation is commonly considered only as an useful computational trick. However, as it was suggested by Hartle and Hawking already in early eighties, Wick rotation may gain physical meaning at the Planck epoch. While such possibility is conceptually interesting, leading to no-boundary proposal, mechanism behind the signature change remains mysterious. In this talk we show that the signature change anticipated by Hartle and Hawking may occur in result of the loop quantum gravity effects. Theory of cosmological perturbations with the effects of quantum holonomies is constructed. It is shown that such theory can be uniquely formulated in the anomaly-free manner. The algebra of quantum constraints turns out to be modified such that the signature is changing from Lorentzian in low curvature regime to Euclidean in high curvature regime. Implications of this phenomenon on propagation of cosmological perturbations are discussed. Possible relations with other approaches to quantum gravity are also outlined.

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Hans-Christian Ruiz (LMU München)

Introduction to Spin Networks and the Decomposition Theorem

In this talk the basic mathematical framework for the algebraic description of spin networks is described. Furthermore, the notion of spherical category and its relation to the diagrammatic representation given by the Temperley-Lieb recoupling theory are presented. The latter, being an important tool for the evaluation of spin networks in terms of the q-deformed 6j-symbols, is related to Moussouris' algorithm and allows the study of non-planar spin networks. For this, basic concepts of topological graph theory are given and the results of calculations regarding different embeddings of the minimal non-planar spin network are presented and discussed.

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Maximilian Poretschkin (Bonn)

Introduction to F-theory

String theory is a promising candidate for a unified description of particle physics and gravity. In the last decades there has been enormeous progress in the understanding how the standard model of particle physics can be obtained from string theory compactifications. However so far string theory is defined as a perturbative series and the access to the strongly coupled regime is difficult. Type IIB string theory admits an SL(2, Z)-symmetry that provides a weak-strong coupling duality. The main idea of F-Theory is to consider the SL(2,Z)-symmetry as the symmetry of an auxiliary torus that is part of an auxiliary space-time. By this it is possible to enter the strongly coupled regime of string compactifications. In this talk I will introduce the general idea of F-theory compactifications and its relation to M- and string theory compactifications. Whenever possible, I will allude to the (super-)gravity point of view.

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Eva Hackmann (Bremen)

Structure and analytical solutions of orbits in axially symmetric space-times

The structure of solutions of the geodesic equations in general axially symmetric space-times can be very complex and differs significantly from the plane conic sections of Newtonian gravity. Each space-time exhibits an individual set of geodesics which allows to conclude from the observation of orbits on the physical properties of the underlying space-time. The complete set of solutions of the geodesic equation in a given space-time can be studied most conveniently by using analytical methods. In the case of type D space-times with separable Hamilton-Jacobi equation the analytical solutions can be constructed in terms of elliptic or the more general hyperelliptic functions. In this talk the structure of orbits and the construction of analytical solutions will be exemplified in some type D space-times.

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James M. Nester (Chung-li, Taiwan)

Good dynamical torsion modes of spin zero: some cosmological exploration

We briefly review the fundamentals of the Poincare gauge theory of gravity (PG), the steps that led to the identification of the PG theory having two good dynamical torsion modes of spin 0, and the development of the most general model with these two dynamical modes. Then some cosmological models are used to explore the dynamics of these spin zero modes.

Reference: Shie, Nester, and Yo, Phys. Rev. D 78, 023522 (2008) [arXiv:0805.3834].

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André Großardt (Bremen)

Schrödinger–Newton equation as a model for self-gravitating systems

In a recent study of the time-dependent Schrödinger-Newton (SN) equation we showed that gravitationally induced inhibitions of dispersion for a Gaussian wave packet of 500 nm width occur for masses of about 1e10 u and above. This is more than six orders of magnitude beyond the results of a former analysis but nevertheless might be a feasible mass range for future molecular interferometry experiments, which where suggested as a method to test the SN equation. In this talk I want to focus on the question if and in what sense the SN equation can be understood as a model for a gravitationally self-interacting quantum system and how it can be derived from known principles. Therefore, I will motivate a WKB-like approximation scheme and show that – at least formally – the SN equation follows as the non-relativistic limit of both the Klein–Gordon and Dirac equation coupled to Einstein gravity.

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