Lovelock gravitation theory is a natural extension of the General Relativity to higher dimensions with the inclusion of only second-order terms correspond to the Einstein–Gauss–Bonnet gravity. In this paper, we find an exact Hayward black hole solution of $D\ge 5$-dimensional spacetime for Einstein–Gauss–Bonnet (EGB) gravity with negative cosmological constant ($\Lambda$) minimally coupled to non-linear electrodynamics for a specific Lagrangian density, namely, EGB-AdS black holes, with additional parameter $e$ because of magnetic charge. Interestingly, it turns out that for each value of GB parameter $\left(\alpha \right)$, there exist a critical $e_E$ such that for $e<e_E$ describe non-extremal black holes with Cauchy ($r_{-}$) and Event horizons ($r_{+}$), while for $e=e_E$ corresponds to an extremal regular black hole with degenerate horizons ($r_{+}=r_{-}=r_E$). Owing to the magnetically charged corrected black hole, the thermodynamic quantities have also been modified, but the entropy does not satisfy the usual area law. A divergence of the specific heat at $r_{+}=r_c$, where the temperature attains maximum value and the Hawking–Page transition is achievable with the stable (unstable) branch for $r_{t1}\le r_{+}<r_c$ ($r_c<r_{+}\le r_{t2}$). Thus, we found Hayward EGB-AdS black holes which do not evaporate completely, but lead to stable double-horizon black hole remnants with vanishing temperature and positive heat capacity.

拉夫洛克引力理论是广义相对论向更高维度的自然延伸，只包含了与爱因斯坦-高斯-贝内特引力相对应的二阶项。在本文中，我们找到了一个精确的Hayward黑洞解$d\ge 5$宇宙常数为负的爱因斯坦-高斯-帽子（EGB）重力的三维时空（$\Lambda$）最小耦合到特定拉格朗日密度的非线性电动力学，即EGB-AdS黑洞，并带有附加参数 $Ë$因为有电荷 有趣的是，事实证明，对于GB参数的每个值$（\alpha ）$，存在一个关键 ${Ë}_{Ë}$ 这样 $Ë<{Ë}_{Ë}$ 用柯西（Cauchy）描述非极端的黑洞（${\mathrm{[R}}_{-}$）和事件范围（${\mathrm{[R}}_{+}$），而 $Ë={Ë}_{Ë}$ 对应于视界退化的极端规则黑洞（${\mathrm{[R}}_{+}={\mathrm{[R}}_{-}={\mathrm{[R}}_{Ë}$）。由于带磁性的校正黑洞，热力学量也已修改，但熵不满足通常的面积定律。比热在${\mathrm{[R}}_{+}={\mathrm{[R}}_C$，其中温度达到最大值，并且可以通过稳定（不稳定）的分支实现Hawking-Page转换 ${\mathrm{[R}}_{Ť\mathrm{1个}}\le {\mathrm{[R}}_{+}<{\mathrm{[R}}_C$ （${\mathrm{[R}}_C<{\mathrm{[R}}_{+}\le {\mathrm{[R}}_{Ť2}$）。因此，我们发现海沃德EGB-AdS黑洞不会完全蒸发，但会导致稳定的双水平黑洞残迹，并且温度和正热容均消失。