发表机构
Universidade Federal de Campina Grande（坎皮纳格兰德联邦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究利用WKB近似和有限差分法，探讨了广义不确定性原理对高维Schwarzschild-Tangherlini黑洞准正则模和阴影的影响，并通过人马座A*观测约束了GUP参数空间。
AI 中文摘要
在这项工作中，我们研究了在$(d+1)$维中，包含广义不确定性原理（GUP）修正的Schwarzschild-Tangherlini黑洞的准正则模和阴影。使用六阶WKB近似，我们计算了$l=1, 2$和$d=3, 4, 5, 6$情况下的准正则频率，并分别分析了无量纲线性GUP参数$\bar{\alpha}$和二次GUP参数$\bar{\beta}$的影响。我们发现，在所考虑的参数范围内，线性修正增加了振荡频率和阻尼率，而二次修正则产生相反的行为。使用有限差分格式，我们获得了时域演化，并发现更高维度导致更快的阻尼，且GUP引起的时域波形修正的可见性取决于初始扰动的激发轮廓，而潜在的准正则谱仍由黑洞决定。最后，我们研究了阴影，并通过不稳定圆零测地线的性质建立了其在eikonal极限下与准正则谱的对应关系。最后，我们将预测的阴影大小与事件视界望远镜对人马座A*的观测进行比较，并利用这些约束来研究允许的GUP参数空间。
英文摘要
In this work, we investigate quasinormal modes and the shadow of a Schwarzschild-Tangherlini black hole in $(d+1)$ dimensions, incorporating corrections arising from the Generalized Uncertainty Principle (GUP). Using the WKB approximation up to sixth order, we calculate the quasinormal frequencies for $l=1, 2$ and $d=3, 4, 5, 6$, and analyze the effects of the dimensionless linear and quadratic GUP parameters $\barα$ and $\barβ$, respectively. We find that the linear correction increases the oscillation frequency and the damping rate, whereas the quadratic correction produces the opposite behavior within the parameter range considered. Using the finite difference scheme, we obtain the time-domain evolution and find that higher dimensions lead to faster damping and that the visibility of GUP-induced modifications to the time-domain waveform depends on the excitation profile of the initial perturbation, whereas the underlying quasinormal spectrum remains determined by the black hole geometry.Furthermore, we investigate the shadow and establish its correspondence with the quasinormal spectrum in the eikonal limit through the properties of the unstable circular null geodesics. Finally, we confront the predicted shadow size with Event Horizon Telescope observations of Sagittarius A* and use these constraints to investigate the allowed GUP parameter space.
CommentsLattex, 17 pages, 9 figures, 4 tables
