By analyzing the energy–momentum relationship of the absorbed fermions dropping into a Reissner–Nordstöm–anti-de Sitter black hole surrounded by dark matter, the laws of thermodynamic and weak cosmic censorship conjecture in the extended phase space are investigated. We find that the first law of thermodynamics is valid. However, the validity of the second law of thermodynamics depends on the density α of the perfect fluid dark matter. In addition, we also find that when the fermions are absorbed, the structures of black hole surrounded by dark matter would not change. Therefore, weak cosmic censorship conjecture holds for the extreme black holes and the non-extreme black holes.

中文翻译：

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暗物质对扩展空间中弱宇宙审查猜想的影响

通过分析被吸收的费米子落入被暗物质包围的Reissner-Nordstöm-anti-de Sitter黑洞的能量-动量关系，研究了扩展相空间中的热力学规律和弱宇宙审查猜想。我们发现热力学第一定律是有效的。然而，热力学第二定律的有效性取决于密度α完美的流体暗物质。此外，我们还发现，当费米子被吸收时，被暗物质包围的黑洞的结构不会发生变化。因此，弱宇宙审查猜想对极端黑洞和非极端黑洞都成立。