标题： 由非线性电磁学源的规则黑洞 显示英文标题

标题： Regular black holes sourced by nonlinear electrodynamics

摘要： 本文是对广义相对论中静态、球对称正则黑洞解的存在性及其基本性质的一个简要回顾，其中引力的来源由非线性电磁场表示，其拉格朗日函数$L$依赖于单一不变量$f = F_{\mu\nu}F^{\mu\nu}$或两个变量：要么是$L(f, h)$（其中$h = {^*}F_{\mu\nu} F^{\mu\nu}$，${^*}F_{\mu\nu}$是$F_{\mu\nu}$的霍奇对偶），要么是$L(f, J)$（其中$J = F_{\mu\nu}F^{\nu\rho} F_{\rho\sigma} F^{\sigma\mu}$）。 讨论了一些非通约定理，揭示了时空不能具有正则中心的条件，其中关于$L(f,J)$理论的定理可能是新的。 这些结果既涉及无视界规则黑洞，也涉及无视界规则粒子状或恒星状物体（孤子）。 因此，在带有电荷$q_e\ne 0$的解中，正则中心的存在仅可能依赖于没有麦克斯韦弱场极限的非线性电动力学（NED）。 如果系统仅包含磁荷$q_m \ne 0$，则具有$L(f)$和$L(f, J)$NED 的正则解，且具有正确的（麦克斯韦）弱场极限是可能的。 然而，证明表明在这种解中，在中心附近的因果性和单位性以及动力学稳定性条件不可避免地会被违反。 讨论了一些特殊情况的例子。 显示英文摘要

摘要： The paper is a brief review on the existence and basic properties of static, spherically symmetric regular black hole solutions of general relativity, where the source of gravity is represented by nonlinear electromagnetic fields with the Lagrangian function $L$ depending on the single invariant $f = F_{\mu\nu}F^{\mu\nu}$ or on two variables: either $L(f, h)$, where $h = {^*}F_{\mu\nu} F^{\mu\nu}$, where ${^*}F_{\mu\nu}$ is the Hodge dual of $F_{\mu\nu}$, or $L(f, J)$, where $J = F_{\mu\nu}F^{\nu\rho} F_{\rho\sigma} F^{\sigma\mu}$. A number of no-go theorems are discussed, revealing the conditions under which the space-time cannot have a regular center, among which the theorems concerning $L(f,J)$ theories are probably new. These results concern both regular black holes and regular particlelike or starlike objects (solitons) without horizons. Thus, a regular center in solutions with an electric charge $q_e\ne 0$ is only possible with nonlinear electrodynamics (NED) having no Maxwell weak field limit. Regular solutions with $L(f)$ and $L(f, J)$ NED, possessing a correct (Maxwell) weak-field limit, are possible if the system contains only a magnetic charge $q_m \ne 0$. It is shown, however, that in such solutions the causality and unitarity as well as dynamic stability conditions are inevitably violated in a neighborhood of the center. Some particular examples are discussed.