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 AdS4 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 [Formula: see text] while Nariai numbers exist and tend to zero for large values of [Formula: see text]. Moreover, we show that there is an effect of [Formula: see text] 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 [Formula: see text], but its value increases with increasing [Formula: see text].

中文翻译：

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具有涂抹质量分布的球对称 AdS 黑洞

在本文中，我们研究了球对称 AdS 黑洞中非交换 NC (3 + 1) 维的热力学性质。研究了使用一般分布质量的AdS时空运动方程的解。结果表明存在AdS4黑洞仅适用于非高斯分布，而对于高斯分布，在宇宙学常数 [公式：见文本] 值较小的情况下不存在 Nariai 数，而对于 [公式：见正文]。此外，我们证明了[公式：见正文]对黑洞霍金温度的影响，当霍金温度趋于零时，这种影响就消失了。最后，事实证明，自由能的行为不随[公式：见正文]的变化而变化，但其值随着[公式：见正文]的增加而增加。