1. 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

2. 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

3. 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

4. Piotr T. Chruściel, Michał Eckstein, Luc Nguyen and Sebastian J. Szybka
Existence of singularities in two-Kerr black holes
Class. Quantum Grav., vol. 28, p. 245017 (2011).
[abstract] [preprint] [journal]

Abstract:
We show that the angular momentum—area inequality 8π|J| ≤ A for weakly stable minimal surfaces would apply to I+-regular many-Kerr solutions, if any existed. Hence, we remove the undesirable hypothesis in the Hennig–Neugebauer proof of non-existence of well-behaved two-component solutions.
*supported by the grant from The John Templeton Foundation

5. Wojciech Czaja, Zdzislaw A. Golda, Andrzej Woszczyna
The acoustic wave equation in the expanding universe. Sachs-Wolfe theorem
The Mathematica Journal, vol. 13 (2011).
[abstract] [journal] [cdf]

Abstract:
This article considers the acoustic field propagating in the radiation-dominated universe of arbitrary space curvature. The field equations are reduced to the d’Alembert equation in an auxiliary static Robertson-Walker spacetime and dispersion relations are discussed. *supported by the grant from The John Templeton Foundation