43. Nicolas Franco
Survey of Gravity in Non-Commutative Geometry
Topology, Quantum fields theory & Cosmology, Hermann, pp. 313-329 (2009).
[abstract] [preprint]

Abstract:
We present a survey of the application of Cones' Non-Commutative Geometry to gravitation. Bases of the theory and Euclidian gravity models are reviewed. Then we discuss the problem of a Lorentzian generalization of the theory and review existing attempts of solution.

44. Sebastian J. Szybka
Chaos and Vacuum Gravitational Collapse
Proceedings of the Spanish Relativity Meeting 2008, AIP Conf. Proc., vol. 1122, pp. 172-178 (2009).
[abstract] [journal]

Abstract:
The numerical evidence for chaotic behavior in vacuum gravitational collapse is presented. The collapse is studied in five dimensional vacuum spacetimes satisfying the cohomogeneity-two triaxial Bianchi type-IX ansatz.

45. A. Sitarz
Twisted Dirac operators over quantum spheres
J.Math.Phys, vol. 49, p. 0335092008 (2008).
[abstract] [preprint] [journal]

Abstract:
We construct new families of spectral triples over quantum spheres, with a particular attention focused on the standard Podles quantum sphere and twisted Dirac operators.

46. A.Sitarz
3 1/2 Lectures on Noncommutative Geometry
Acta Polytechnica, vol. 48, pp. 34-55 (2008).
[abstract] [journal] [download]

Abstract:
We present a short overview of noncommutative geometry. Starting with C* algebras and noncommutative differential forms we pass to K-theory, K-homology and cyclic (co)homology, and we finish with the notion of spectral triples and the spectral action.

47. D.Essouabri, B.Iochum, C.Levy, A.Sitarz
Spectral action on noncommutative torus
Journal of Noncommutative Geometry, vol. 2, pp. 53-123 (2008).
[abstract] [preprint] [journal] [download]

Abstract:
The spectral action on the noncommutative torus is obtained using a Chamseddine–Connes formula via computations of zeta functions. The importance of a Diophantine condition is outlined. Several results on holomorphic continuation of series of holomorphic functions are obtained in this context.

48. J.Gruszczak
Discrete Spectrum of the Deficit Angle and the Differential Structure of a Cosmic String
Int J Theor Phys, vol. 47, pp. 2911-2923 (2008).
[abstract]

Abstract:
Differential properties of Klein-Gordon and electromagnetic fields on the space-time of a straight cosmic string are studied with the help of methods of the differential space theory. It is shown that these fields are smooth in the interior of the cosmic string space-time and that they loose this property at the singular boundary except for the cosmic string space-times with the following deficit angles: \delta = 2π(1 −1/n), n = 1, 2, . . . . A connection between smoothness of fields at the conical singularity and the scalar and electromagnetic conical bremsstrahlung is discussed. It is also argued that the smoothness assumption of fields at the singularity is equivalent to the Aliev and Gal’tsov “quantization” condition leading to the above mentioned discrete spectrum of the deficit angle.