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37. Nicolas Franco
Towards a noncommutative version of Gravitation
AIP Conference Proceedings, vol. 1241, pp. 588-594 (2010).
[abstract] [preprint] [journal]

Alain Connes' noncommutative theory led to an interesting model including both Standard Model of particle physics and Euclidean Gravity. Nevertheless, an hyperbolic version of the gravitational part would be necessary to make physical predictions, but it is still under research. We shall present the difficulties to generalize the model from Riemannian to Lorentzian Geometry and discuss key ideas and current attempts.

38. A. Sitarz
Quasi-Dirac Operators and Quasi-Fermions
J. Phys. A: Math. Theor., vol. 42, p. 155201 (2009).
[abstract] [preprint] [journal] [download]

We investigate examples of quasi-spectral triples over two-dimensional commutative sphere, which are obtained by modifying the order-one condition. We find equivariant quasi-Dirac operators and prove that they are in a topologically distinct sector than the standard Dirac operator.

39. A.Sitarz
Spectral action and neutrino mass
European Physics Letters, vol. 86, p. 10007 (2009).
[abstract] [preprint] [journal] [download]

We propose the extension of the spectral action principle to fermions and show that the neutrino mass terms then appear naturally as next-order corrections.

40. B.Iochum, C.Levy, A.Sitarz
Spectral action on SUq(2)
Commun. Math. Phys., vol. 289, pp. 107-155 (2009).
[abstract] [preprint] [journal] [download]

The spectral action on the equivariant real spectral triple over A(SUq(2))SUq(2) is computed explicitly. Properties of the differential calculus arising from the Dirac operator are studied and the results are compared to the commutative case of the sphere \mathbbS3S3.

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

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.

42. 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]

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.

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