37. Nicolas Franco
Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry
SIGMA, vol. 6, 064 (2010).
[abstract] [preprint] [journal]

Abstract:
Connes' noncommutative Riemannian distance formula is constructed in two steps, the first one being the construction of a path-independent geometrical functional using a global constraint on continuous functions. This paper generalizes this first step to Lorentzian geometry. We show that, in a globally hyperbolic spacetime, a single global timelike eikonal condition is sufficient to construct a path-independent Lorentzian distance function.

38. Piotr T. Chruściel, Michał Eckstein, Sebastian J. Szybka
On smoothness of Black Saturns
Journal of High Energy Physics, vol. 2010, pp. 1-39 (2010).
[abstract] [preprint] [journal]

Abstract:
We prove smoothness of the domain of outer communications (d.o.c.) of the Black Saturn solutions of Elvang and Figueras. We show that the metric on the d.o.c. extends smoothly across two disjoint event horizons with topology R x S^3 and R x S^1 x S^2. We establish stable causality of the d.o.c. when the Komar angular momentum of the spherical component of the horizon vanishes, and present numerical evidence for stable causality in general.

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

Abstract:
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.

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

Abstract:
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.

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

Abstract:
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.

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

Abstract:
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.