A regular static, spherically symmetric electrically charged black hole solution of general relativity coupled to a new theory for nonlinear electrodynamics is presented. This theory has the interesting feature that, at far distances from the black hole, in the weak field limit, the theory reduces to Maxwell Lagrangian with Heisenberg–Euler correction term of quantum electrodynamics. The singular center of the black hole is replaced by flat, de Sitter, or anti de Sitter space, if the spacetime in which the black hole is embedded is asymptotically flat, de Sitter, or anti de Sitter, respectively. Requiring the correspondence to Heisenberg–Euler Lagrangian at large distances, in the weak field limit, we find that (i) a minimum mass is required for the formation of an event horizon for the regular static, spherically symmetric solution of the theory, and, (ii) the mass of the solution must be quantized. We also study the basic thermodynamic properties of the black hole solution and show that they are qualitatively similar to those of Reissner–Nordström black hole.

中文翻译：

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一种新的非线性电动力学和带电规则黑洞

提出了与非线性电动力学新理论耦合的广义相对论的规则静态、球对称带电黑洞解。该理论有一个有趣的特点，即在远离黑洞的地方，在弱场极限下，该理论可以简化为具有量子电动力学的海森堡-欧拉校正项的麦克斯韦拉格朗日。如果黑洞嵌入的时空分别是渐近平坦的、德西特或反德西特空间，则黑洞的奇异中心将被平坦、德西特或反德西特空间所取代。需要在远距离与海森堡-欧拉拉格朗日的对应关系，在弱场极限下，我们发现（i）对于该理论的常规静态球对称解，形成事件视界需要最小质量，并且，(ii) 溶液的质量必须被量化。我们还研究了黑洞解的基本热力学性质，并表明它们在性质上与 Reissner-Nordström 黑洞的性质相似。