Spherically symmetric AdS black holes with smeared mass distribution

In this paper, we study the thermodynamics properties of noncommutative NC (3 + 1)-dimensional in the spherically symmetric AdS black holes. The solution of equations of motion in AdS spacetime using a general distribution mass is studied. The results show that there exist AdS(4) black holes only for the non-Gaussian distributions, while for the Gaussian distributions, Nariai numbers do not exist in case of small values of cosmological constant Lambda while Nariai numbers exist and tend to zero for large values of Lambda. Moreover, we show that there is an effect of Lambda on the Hawking temperature of black hole and this effect disappears when the Hawking temperature tends to zero. Finally, it turns out that the behavior of free energy does not change with the change of Lambda but its value increases with increasing Lambda.