We derive an exact solution for a spherically symmetric Bardeen black hole surrounded by perfect fluid dark matter (PFDM). By treating the magnetic charge g and dark matter parameter as thermodynamic variables, we find that the first law of thermodynamics and the corresponding Smarr formula are satisfied. The thermodynamic stability of the black hole is also studied. The results show that there exists a critical radius where the heat capacity diverges, suggesting that the black hole is thermodynamically stable in the range . In addition, the critical radius increases with the magnetic charge g and decreases with the dark matter parameter . Applying the Newman-Janis algorithm, we generalize the spherically symmetric solution to the corresponding rotating black hole. With the metric at hand, the horizons and ergospheres are studied. It turns out that for a fixed dark matter parameter , in a certain range, with the increase of the rotation parameter a and magnetic charge g, the Cauchy horizon radius increases while the event horizon radius decreases. Finally, we investigate the energy extraction by the Penrose process in a rotating Bardeen black hole surrounded by PFDM.

我们推导出一个被完美流体暗物质 (PFDM) 包围的球对称巴丁黑洞的精确解。通过将磁荷g和暗物质参数作为热力学变量，我们发现满足热力学第一定律和相应的Smarr公式。还研究了黑洞的热力学稳定性。结果表明，存在一个热容发散的临界半径，表明黑洞在该范围内是热力学稳定的。此外，临界半径随磁荷g增大而随暗物质参数减小. 应用 Newman-Janis 算法，我们将球对称解推广到相应的旋转黑洞。有了手头的度量，就研究了视野和能层。事实证明，对于固定的暗物质参数，在一定范围内，随着旋转参数a和磁荷g的增加，柯西视界半径增加，而事件视界半径减小。最后，我们研究了彭罗斯过程在被 PFDM 包围的旋转 Bardeen 黑洞中的能量提取。