In this paper, we derived an exact solution of the spherically symmetric Hayward black hole surrounded by perfect fluid dark matter (PFDM). By applying the Newman–Janis algorithm, we generalized it to the corresponding rotating black hole. Then, we studied the shadows of rotating Hayward black hole in PFDM. The apparent shape of the shadow depends upon the black hole spin a, the magnetic charge Q and the PFDM intensity parameter k(k < 0). The shadow is a perfect circle in the non-rotating case (a = 0) and a deformed one in the rotating case (a≠0). For a fixed value of a, the size of the shadow increases with the increasing |k|, but decreases with the increasing Q. We further investigated the black hole emission rate. We found that the emission rate decreases with the increasing |k| (or Q) and the peak of the emission shifts to lower frequency. Finally, we discussed the observational prospects corresponding to the supermassive black hole Sgr A∗ at the center of the Milky Way.

中文翻译：

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完美流体暗物质中旋转和非线性带磁黑洞的阴影投射

在本文中，我们推导出了完美流体暗物质 (PFDM) 包围的球对称海沃德黑洞的精确解。通过应用 Newman-Janis 算法，我们将其推广到相应的旋转黑洞。然后，我们研究了 PFDM 中旋转的海沃德黑洞的阴影。阴影的外观形状取决于黑洞的自旋一种, 磁荷问和 PFDM 强度参数ķ(ķ < 0). 在不旋转的情况下，阴影是一个完美的圆(一种 = 0)和一个变形的旋转外壳(一种≠0). 对于固定值一种, 阴影的大小随着增加|ķ|, 但随着增加而减少问. 我们进一步研究了黑洞发射率。我们发现排放率随着增加|ķ|（要么问) 并且发射的峰值转移到较低的频率。最后，我们讨论了超大质量黑洞Sgr A对应的观测前景*在银河系的中心。