Einstein-Gauss-Bonnet (EGB) gravity is an outcome of quadratic curvature corrections to the Einstein-Hilbert gravity action in the form of a Gauss-Bonnet (GB) term in $ D > 4$ dimensions and EGB gravity is topologically invariant in $4D$. Recently a number of ways have been proposed for regularizing, a $ D \to 4 $ limit of EGB, for nontrivial gravitational dynamics in $ 4D $. Motivated by the importance of anti-de Sitter gravity/conformal field theory correspondence (AdS/CFT), we analyze black holes with AdS asymptotic to regularized $4D$ EGB gravity coupled to the nonlinear electrodynamics (NED) field. For a static spherical symmetric \textit{ansatz} the field equations are solved exactly for a NED Lagrangian - namely NED charged AdS black holes in $4D$ EGB gravity which retains several known solutions. Owing to the NED charge corrected EGB black holes, the thermodynamic quantities are also modified and the entropy does not obey the usual area law. We calculate the heat capacity and Helmholtz free energy, in terms of horizon radii, to investigate both local and global thermodynamic stability of black holes. We observe a secondary Hawking-Page transition between the smaller thermally favored black hole and thermal AdS space. Our results show that the behavior of Hawking's evaporation abruptly halts at a smaller radii regime such that the black holes do have a thermodynamically stable remnant with vanishing temperature.

中文翻译：

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与非线性电动力学耦合的 4D EGB 引力中 AdS 黑洞的相变

Einstein-Gauss-Bonnet (EGB) 引力是对爱因斯坦-希尔伯特引力作用进行二次曲率修正的结果，其形式为 $ D > 4$ 维度的 Gauss-Bonnet (GB) 项，并且 EGB 引力在 $4 中是拓扑不变的美元。最近提出了许多正则化的方法，EGB 的 $ D \ 到 4 $ 限制，用于 $ 4D $ 中的非平凡引力动力学。受反德西特引力/共形场理论对应 (AdS/CFT) 重要性的启发，我们分析了 AdS 渐近到正则化 $4D$ EGB 引力耦合到非线性电动力学 (NED) 场的黑洞。对于静态球对称 \textit{ansatz}，场方程精确求解为 NED 拉格朗日 - 即 NED 带电的 AdS 黑洞在 $4D$ EGB 引力中保留了几个已知的解决方案。由于 NED 电荷校正 EGB 黑洞，热力学量也被修改，熵不遵守通常的面积定律。我们根据视界半径计算热容量和亥姆霍兹自由能，以研究黑洞的局部和全局热力学稳定性。我们观察到较小的受热影响的黑洞和热 AdS 空间之间的二次霍金页过渡。我们的结果表明，霍金的蒸发行为在较小的半径范围内突然停止，因此黑洞确实具有温度消失的热力学稳定残余物。研究黑洞的局部和全局热力学稳定性。我们观察到较小的受热影响的黑洞和热 AdS 空间之间的二次霍金页过渡。我们的结果表明，霍金的蒸发行为在较小的半径范围内突然停止，因此黑洞确实具有温度消失的热力学稳定残余物。研究黑洞的局部和全局热力学稳定性。我们观察到较小的受热影响的黑洞和热 AdS 空间之间的二次霍金页过渡。我们的结果表明，霍金的蒸发行为在较小的半径范围内突然停止，因此黑洞确实具有温度消失的热力学稳定残余物。