A non commutative model for a mini black hole

Abstract

We analyze the static and spherically symmetric perfect fluid solutions of Einstein field equations inspired by the non commutative geometry. In the framework of the non commutative geometry this solution is interpreted as a mini black hole which has the Schwarzschild geometry outside the event horizon, but whose standard central singularity is replaced by a self-gravitating droplet. The energy-momentum tensor of the droplet is of the anisotropic fluid obeying a nonlocal equation of state. The radius of the droplet is finite and the pressure, which gives rise to the hydrostatic equilibrium, is positive definite in the interior.

10 pages, 2 figures, bibliography enlarged, reference in the conclusion fixed, some typos corrected

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