标题： 五维旋转和暗能量黑洞及其超阴影 显示英文标题

标题： Five dimensional rotating and Quintessence black hole and their hypershadows

摘要： 我们提出了一种新的五维旋转的暗能量黑洞解。 为了获得这个解，我们采用了雅尼思-纽曼算法的$5D$版本，该版本结合了霍普夫分岔。 暗能量参数$w_q$的变化导致几何结构从一个由宇宙视界包围的规则旋转宇宙转变为一个奇异的旋转几何结构，这可以表示裸奇点、奇异极端黑洞或同时具有内视界和外视界（事件视界）的奇异黑洞。 我们还确定了能层的性质。 在研究阴影时，我们采用了一种新方法，其中人类观察到的$2D$阴影对应于$3D$阴影的截面。 我们分析了暗能量如何影响黑洞阴影的大小和形状，表明增加暗能量强度会减小阴影半径，这与$4D$中已知的结果相反。 我们还提出了一种推测性方法，在考虑事件视界望远镜（EHT）关于四维超大质量黑洞 M87 阴影的约束条件下，测试五维情景中的阴影行为。 我们识别出理论上的$5D$结果可能与这些观测约束一致的情况。 我们还测试了我们阴影的圆形偏差，发现无论是否有暗能量，结果都满足边界$\Delta C \leq 0.1$。 最后，我们确定了支持该解所需的能量条件。 显示英文摘要

摘要： We present a new five-dimensional rotating quintessence black hole solution. To obtain this, we employ the $5D$ version of the Janis Newman algorithm, which incorporates the Hopf bifurcation. The variation of the quintessence parameter $w_q$ causes the geometry to transition from a regular rotating universe surrounded by a cosmological horizon to a singular rotating geometry, which can represent a naked singularity, a singular extremal black hole, or a singular black hole with both an inner and an outer (event) horizon. We have also determined the properties of the ergosphere. For the study of the shadow, we followed a novel approach in which the $2D$ shadow observed by humans corresponds to cross sections of the $3D$ shadow. We analyzed how quintessence affects both the size and shape of the black hole shadow, showing that increasing the quintessence strength reduces the shadow radius, contrary to the known results in $4D$. We also propose a speculative methodology to test the shadow behavior in five dimensional scenarios, in light of the constraints provided by the Event Horizon Telescope (EHT) concerning the shadow of the four-dimensional supermassive black hole M87. We identify scenarios in which the theoretical $5D$ results could be consistent with these observational constraints. We have also tested the circularity deviation of our shadows, finding that the results satisfy the bound $\Delta C \leq 0.1$ both in the case with quintessence and in the limiting case without quintessence. Finally, we determine the energy conditions required to support the solution.