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We present a toy model of a fuzzy Schwarzschild space slice (as a noncommutative manifold), in which quantum mean values and quantum quasi-coherent states (states minimizing the quantum uncertainties) have properties close to the classical slice of ( r, θ) Schwarzschild coordinates (the so-called Flamm’s paraboloid). This fuzzy Schwarzschild slice is built as a deformation of the noncommutative plane. Quantum time observables are introduced to add a time quantization in the model. We study the structure of the quasi-coherent state of the fuzzy Schwarzschild slice with respect to the quasi-coherent state and the deformation states of the noncommutative plane. The quantum dynamics of a fermion interacting with a fuzzy black hole described by the present model is studied. In particular, we study the decoherence effects appearing in the neighborhood of the fuzzy event horizon. An extension of the model to describe a quantum wormhole is also proposed, where we show that fermions cross the wormhole not by traveling by its internal space but by quantum tunneling, in accordance with the non-traversable character of classical Einstein–Rosen bridges.

International audience; The newly discovered property of Effective Locality bears on QCD non-perturbative fermionic Green’s functions. It has produced a certain number of interesting tree level results, while remaining somewhat enigmatic. Recalling and enlarging its derivation, focus is put on a possible deep meaning of effective locality which turns out to be independent of any form of representation used for the interacting fermionic fields in a background gluonic configuration. As the latter are implemented though, other remarkable consequences of effective locality come about which will be discussed.