发表机构
Sapienza Università di Roma; Université Paris Cité; CNRS（罗马第一大学; 巴黎西岱大学; 法国国家科学研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究证明在爱因斯坦-非线性电动力学理论中，非奇异双荷黑洞的中心正则性、无鬼场与角向梯度稳定性不可兼得，正则性必然导致梯度不稳定性，需扩展理论以规避。
AI 中文摘要
经典黑洞解所展现的时空奇点，预期会被超出广义相对论有效范围的高能效应所治愈。另一方面，存在众所周知的经典理论允许非奇异黑洞解的例子。最突出的例子是通过在广义相对论的引力扇区中补充一个最小耦合的非线性电动力学扇区而得到的。最近已证明，在爱因斯坦-非线性电动力学框架中，纯电/纯磁的非奇异黑洞总是受到梯度不稳定性的困扰。在这项工作中，我们推导了静态、球对称双荷解的线性扰动的二次作用量，这些解属于对两个不变量都有一般依赖性的爱因斯坦-非线性电动力学理论。我们表明，中心的正则性、无鬼场以及角向梯度稳定性不能同时成立：在任意接近正则中心处，至少有一个光子极化具有负的平方角向传播速度。我们进一步表明，正则性驱动一个电磁动力学本征值在中心处趋于零，这可能限制了核心附近的微扰控制。规避这一障碍需要扩展理论，例如通过引入额外的自由度。
英文摘要
Spacetime singularities displayed by classical black hole solutions are expected to be cured by high-energy effects, beyond the regime of validity of General Relativity. On the other hand, there are well-known examples of classical theories allowing for nonsingular black hole solutions. The most prominent is obtained by complementing the gravitational sector of General Relativity with a minimally coupled nonlinear-electrodynamics sector. It has recently been shown that purely electric/purely magnetic nonsingular black holes in an Einstein-nonlinear-electrodynamics setup are always plagued by a gradient instability. In this work, we derive the quadratic action for linear perturbations of static, spherically symmetric dyonic solutions of Einstein-nonlinear-electrodynamics theories with a general dependence on both invariants. We show that regularity of the center, absence of ghosts and angular gradient stability cannot hold simultaneously: arbitrarily close to a regular center, at least one photon polarization has a negative squared angular propagation speed. We further show that regularity drives one electromagnetic kinetic eigenvalue to zero at the center, which may limit perturbative control near the core. Evading the obstruction requires extending the theory, for example by introducing additional degrees of freedom.
Comments24 pages
