A non commutative model for a mini black hole

Understand

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.