A model of radiating black hole in noncommutative geometry

The phenomenology of a radiating Schwarzschild black hole is analyzed in a noncommutative spacetime. It is shown that noncommutativity does not depend on the intensity of the curvature. Thus we legitimately introduce noncommutativity in the weak field limit by a coordinate coherent state approach. The new interesting results are the following: i) the existence of a minimal non-zero mass to which black hole can shrink; ii) a finite maximum temperature that the black hole can reach before cooling down to absolute zero; iii) the absence of any curvature singularity. The proposed scenario offers a possible solution to conventional difficulties when describing terminal phase of black hole evaporation. In 1975 Hawking showed that a black hole is able to emit radiation and thus to evaporate [1]. This is one of most intriguing phenomenon in the theory of gravitation, which, after 30 years still remains under debate in particular for what concerns the mysterious explosive end of radiating black holes ( see [2] for a recent review with an extensive reference list ). The black hole phenomenology is part of a larger research area, whose final goal is the formulation of a full quantum theory of gravity. In spite of the promising results that string theory has had in quantizing gravity, the actual calculations of the Hawking radiation are currently obtained by means of quantum field theory in curved space [3]. In fact the black hole evaporation occurs in a semiclassical regime, namely when the density of gravitons is lower than that of the matter field quanta. In spite of this achievements the divergent behavior of the black hole temperature in the final stage of the evaporation remains rather obscure. Indeed in this extreme regime stringy effects cannot be neglected. Recently an improved version of field theory on a noncommutative space time manifold has been proposed as a cheaper way to reproduce the stringy phenomenology, at least in the low energy