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19. Nicolas Franco, Michał Eckstein
An algebraic formulation of causality for noncommutative geometry
Class. Quantum Grav., vol. 30, p. 135007 (2013).
[abstract] [preprint] [journal]

We propose an algebraic formulation of the notion of causality for spectral triples corresponding to globally hyperbolic manifolds with a well defined noncommutative generalization. The causality is given by a specific cone of Hermitian elements respecting an algebraic condition based on the Dirac operator and a fundamental symmetry. We prove that in the commutative case the usual notion of causality is recovered. We show that, when the dimension of the manifold is even, the result can be extended in order to have an algebraic constraint suitable for a Lorentzian distance formula.

20. Christa R. Ölz, Sebastian J. Szybka
Conformal and projection diagrams in LaTeX
[abstract] [preprint]

In general relativity, the causal structure of space-time may sometimes be depicted by conformal Carter-Penrose diagrams or a recent extension of these - the projection diagrams. The introduction of conformal diagrams in the sixties was one of the progenitors of the golden age of relativity. They are the key ingredient of many scientific papers. Unfortunately, drawing them in the form suitable for LaTeX documents is time-consuming and not easy. We present below a library that allows one to draw an arbitrary conformal diagram in a few simple steps.

21. A. Gierzkiewicz, K. Wójcik
Lefschetz sequences and detecting of periodic points
Discrete and Continuous Dynamical Systems - Series A, vol. 32, pp. 81-100 (2012).


22. 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]

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

23. 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]

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

24. 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 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

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