19. Andrzej Sitarz
On the geometry of kappa-deformation
International Journal of Geometric Methods in Modern Physics, vol. 9, pp. 1261011-1261021 (2012).
[abstract] [journal] [download]

Abstract:
We present a brief outline of recent and new results on the mathematical structure underlying the kappa-deformed space. We suggest to turn attention to the observable C*-algebra of kappa-deformed coordinates and its Galilean symmetries. *supported by the grant from The John Templeton Foundation

20. Heller, Michael; Pysiak, Leszek; Sasin, Wiesław
Quantum effects in a noncommutative Friedman world model
Canadian Journal of Physics, vol. 90, pp. 223-228 (2012).
[abstract] [journal] [download]

Abstract:
We present a noncommutative version of the closed Friedman world model and show how its classical space–time geometry can be expressed in terms of typically quantum mathematical structures, namely in terms of an operator algebra on a family of Hilbert spaces. The operator algebra can be completed to the von Neumann algebra , but the geometry cannot be prolonged from to . This mathematical fact is a stumbling block in creating full quantum gravity theory. Two effects appearing in this model, generation of matter and probabilistic properties of singularities, are also discussed. *supported by the grant from The John Templeton Foundation

21. Leszek M. Sokołowski
On the twin paradox in static spacetimes: I. Schwarzschild metric
General Relativity and Gravitation, vol. 44, pp. 1267-1283 (2012).
[abstract] [preprint]

Abstract:
Abstract Motivated by a conjecture put forward by Abramowicz and Bajtlik we reconsider the twin paradox in static spacetimes. According to a well known theorem in Lorentzian geometry the longest timelike worldline between two given points is the unique geodesic line without points conjugate to the initial point on the segment joining the two points. We calculate the proper times for static twins, for twins moving on a circular orbit (if it is a geodesic) around a centre of symmetry and for twins travelling on outgoing and ingoing radial timelike geodesics.We show that the twins on the radial geodesic worldlines are always the oldest ones and we explicitly find the the conjugate points (if they exist) outside the relevant segments. As it is of its own mathematical interest, we find general Jacobi vector fields on the geodesic lines under consideration. In the first part of the work we investigate Schwarzschild geometry. Keywords twin paradox · static spacetimes · Jacobi fields · conjugate points *supported by the grant from The John Templeton Foundation

22. P. Olczykowski, A.Sitarz
K-theory of noncommutative Bieberbach manifolds,
(2012).
[abstract] [preprint]

Abstract:
We compute K-theory of noncommutative Bieberbach manifolds, which quotients of a three-dimensional noncommutative torus by a free action of a cyclic group Z_N, N = 2; 3; 4; 6.

23. Piotr T. Chruściel, Christa R. Ölz, Sebastian J. Szybka
Space-time diagrammatics
Phys. Rev. D: Part. Fields , vol. 86, p. 124041 (2012).
[abstract] [preprint] [journal] [download]

Abstract:
We introduce a new class of two-dimensional diagrams, the \emph{projection diagrams}, as a tool to visualize the global structure of space-times. We construct the diagrams for several metrics of interest, including the Kerr-Newman - (anti) de Sitter family, with or without cosmological constant, and the Emparan-Reall black rings.

24. Andrzej Sitarz
Causality and Noncommutativity
Conference "The Causal Universe", vol. xxx, pp. xxx-xxx (2012).
[abstract] [download]

Abstract:
Noncommutative Geometry oers a modern mathematical approach to the formulation of physical models, which comprise gravity and gauge theories. We review its basic ideas, applications to models with Lorentzian geometry and challenges it poses to our understanding of causality.