We investigate the behavior of a noncommutative radiating Schwarzschild black hole. It is shown that coordinate noncommutativity cures usual problems encountered in the description of the terminal phase of black hole evaporation. More in detail, we find that: the evaporation end-point is a zero temperature extremal black hole even in the case of electrically neutral, non-rotating, objects; there exists a finite maximum temperature that the black hole can reach before cooling down to absolute zero; there is no curvature singularity at the origin, rather we obtain a regular DeSitter core at short distance.Comment: 7 pages, Revtex, 4 eps figures, final version, accepted for publication in Phys.Lett.

Abstract. We formulate Feynman path integral on a non commutative plane using coherent states. The propagator for a free particle exhibits UV cut-off induced by the parameter of non commutativity.

We find a new, non-commutative geometry inspired, solution of the coupled EinsteinMaxwell field equations describing a variety of charged, self-gravitating objects, including extremal and non-extremal black holes. The metric smoothly interpolates between deSitter geometry, at short distance, and Reissner-Nordstrøm geometry far away from the origin. Contrary to the ordinary Reissner-Nordstrøm spacetime there is no curvature singularity in the origin neither "naked" nor shielded by horizons. We investigate both Hawking process and pair creation in this new scenario.In a recent paper we obtained a non-commutative geometry inspired solution of the Einstein equation smoothly interpolating between a deSitter core around the origin and an ordinary Schwarzschild spacetime at large distance 1 email: ansoldi@trieste.infn.it 2

Ultraviolet finite quantum field theory on even dimensional noncommutative spacetime is formulated using coordinate coherent states. 2d spacetime is foliated into families of orthogonal, non commutative, two-planes. Lorentz invariance is recovered if one imposes a single non commutative parameter θ in the theory. Unitarity is checked at the one-loop level and no violation is found. Being UV finite NCQFT does not present any UV/IR mixing.

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