This paper explores the influence of special type of higher order generalized uncertainty principle on the thermodynamics of five-dimensional black hole in Einstein–Gauss–Bonnet gravity coupled to nonlinear electrodynamics. We examine the corrected thermodynamical properties of the black hole with some interesting limiting cases k → 0 and α → 0 and compared our results with usual thermodynamical relations. We observe that the influence of GUP correction stabilizes the BH and BH solution remains physical throughout the region of horizon radius. In this framework, we also uncover the relationship of shadow radius and quasinormal modes of the mentioned black hole. We conclude that shadow radius of our considered black hole is a perfect circle and it decreases with increasing values of charge and Gauss–Bonnet parameter. We also verify the inverse relation between the quasinormal modes frequencies and shadow radius, i.e. quasinormal modes should increase with increasing values of Gauss–Bonnet parameter and electric charge.

中文翻译：

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高斯-博内引力中带电 AdS 黑洞的扩展 GUP 校正热力学、阴影半径和准正规模式

本文探讨了特殊类型的高阶广义不确定性原理对爱因斯坦-高斯-博内重力耦合非线性电动力学中五维黑洞热力学的影响。我们用一些有趣的极限情况检查了黑洞的校正热力学性质ķ → 0和α → 0并将我们的结果与通常的热力学关系进行比较。我们观察到 GUP 校正的影响稳定了 BH 和 BH 解决方案在整个地平线半径区域保持物理。在这个框架中，我们还揭示了上述黑洞的阴影半径和准正规模式的关系。我们得出结论，我们考虑的黑洞的阴影半径是一个完美的圆，它随着电荷值和 Gauss-Bonnet 参数的增加而减小。我们还验证了准正态模式频率和阴影半径之间的反比关系，即准正态模式应该随着 Gauss-Bonnet 参数和电荷值的增加而增加。