We obtain an exact spherically symmetric and magnetically charged black hole solution in 4D Einstein-Gauss-Bonnet gravity coupled with rational nonlinear electrodynamics. The thermodynamics of our model is studied. We calculate the Hawking temperature and the heat capacity of the black hole. The phase transitions occur in the point where the Hawking temperature possesses an extremum. We show that black holes are thermodynamically stable at some range of event horizon radii when the heat capacity is positive. The logarithmic correction to the Bekenstein-Hawking entropy is obtained.

中文翻译：

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具有有理非线性电动力学的爱因斯坦-高斯-博内引力

我们在 4D Einstein-Gauss-Bonnet 引力耦合有理非线性电动力学中获得了精确的球对称和磁荷电黑洞解。研究了我们模型的热力学。我们计算了霍金温度和黑洞的热容量。相变发生在霍金温度具有极值的点。我们表明，当热容为正时，黑洞在某些事件视界半径范围内是热力学稳定的。获得对 Bekenstein-Hawking 熵的对数校正。