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In the context of noncommutative (NCG) gauge gravity, and using a cosmic time power law formula for the scale factor, a Friedman-Robertson-Walker (FRW) like metric is obtained. Within the fermions tunneling effect approach and depending on the various intervals of the power parameter, expressions of the apparent horizon are also derived. It is shown that in some regions of the parameter space, a pure NCG trapped horizon does exist leading to new interpretation of the role played by the noncommutativity of the space-time. [ABSTRACT FROM AUTHOR]

We refine the reconstruction theorem for almost-commutative spectral triples to a result for real almost-commutative spectral triples, clarifying in the process both concrete and abstract definitions of real commutative and almost-commutative spectral triples. In particular, we find that a real almost-commutative spectral triple algebraically encodes the commutative *-algebra of the base manifold in a canonical way, and that a compact oriented Riemannian manifold admits real (almost-)commutative spectral triples of arbitrary KO-dimension. Moreover, we define a notion of smooth family of real finite spectral triples and of the twisting of a concrete real commutative spectral triple by such a family, with interesting KK-theoretic and gauge-theoretic implications. [ABSTRACT FROM AUTHOR]

In this review article we discuss some of the applications of noncommutative geometry in physics that are of recent interest, such as noncommutative many-body systems, noncommutative extension of Special Theory of Relativity kinematics, twisted gauge theories and noncommutative gravity. [ABSTRACT FROM AUTHOR]

After a short introduction, we show how the canonical formalism is constructed in space-time noncommutative theories such that it allows defining the notion of first-class constraints and analyzing gauge symmetries. We use this formalism to noncommutatively deform the two-dimensional string gravity (also known as the Witten black hole). [ABSTRACT FROM AUTHOR]

In this paper, we apply Connes' noncommutative geometry and the Seiberg–Witten map to a discrete noncommutative space consisting of n copies of a given noncommutative space Rm. The explicit action functional of gauge fields on this discrete noncommutative space is obtained. [ABSTRACT FROM AUTHOR]