A modified Hayward metric of magnetically charged black hole space–time based on rational nonlinear electrodynamics with the Lagrangian ℒ = −ℱ/(1 + 2βℱ) is considered. We introduce the fundamental length, characterizing quantum gravity effects. If the fundamental length vanishes the general relativity coupling to rational nonlinear electrodynamics is recovered. We obtain corrections to the Reissner–Nordström solution as the radius approaches infinity. The metric possesses a de Sitter core without singularities as r → 0. The Hawking temperature and the heat capacity are calculated. It was shown that phase transitions occur and black holes are thermodynamically stable at some event horizon radii. We demonstrate that curvature invariants are bounded and the limiting curvature conjecture takes place.

中文翻译：

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有理非线性电动力学的磁化黑洞正则模型

基于拉格朗日有理非线性电动力学的带磁黑洞时空修正海沃德度量ℒ = -ℱ/(1 + 2βℱ)被认为。我们介绍了基本长度，描述了量子引力效应。如果基本长度消失，广义相对论与有理非线性电动力学的耦合就会恢复。当半径接近无穷大时，我们对 Reissner-Nordström 解进行了修正。该度量具有没有奇点的德西特核r → 0. 计算霍金温度和热容量。结果表明，发生相变并且黑洞在某些事件视界半径处是热力学稳定的。我们证明曲率不变量是有界的，并且发生了极限曲率猜想。