The Weak Gravity Conjecture (WGC) predicts that in quantum gravity there should exist overcharged states, that is states with charge larger than their mass. Extending this to large masses and charges, we are expecting similar overcharged classical solutions. This has been demonstrated in higher-derivative extensions of General Relativity. In this paper we investigate the existence of overcharged solutions in General Relativity. We study the dynamics of a thin shell of mass m and charge Q under the action of its own gravitational and U(1) fields. We show that shells with surface energy σ and pressure P obeying P=wσ with 0⩽w⩽1 are necessarily undercharged m⩾|Q| and always collapse to form Reissner–Nordström black holes. Nevertheless, if −1⩽w<0 , we find that overcharged m⩽|Q| shells exist, which however, are inevitably stabilized at finite radial distance. Therefore they never form naked singularities in accordance with cosmic censorship and the conjectured relation between cosmic censorship and the WGC. An intriguing consequence of the existence of such overcharged shells is that gravitational modes may form bound states due to the peculiar form of the Regge–Wheeler–Zerilli potential. This might lead to gravitational traps close the surface of near-overcharged shells.

中文翻译：

---

弱引力猜想、超载贝壳和引力陷阱

弱引力猜想（WGC）预测，在量子引力中应该存在过荷态，即电荷大于其质量的态。将其扩展到大质量和大电荷，我们期待类似的过度充电的经典解决方案。这已经在广义相对论的高导数扩展中得到了证明。在本文中，我们研究了广义相对论中超载解的存在性。我们研究质量薄壳的动力学米并充电问在自身引力的作用下U(1) 领域。我们证明具有表面能的壳σ和压力磷服从 磷=wσ 和 0⩽w⩽1 必然收费不足 米⩾|问| 并且总是会塌缩形成赖斯纳-诺德斯特伦黑洞。尽管如此，如果 -1⩽w<0 ，我们发现多收费了 米⩽|问| 壳是存在的，但是它们不可避免地稳定在有限的径向距离处。因此，根据宇宙审查制度以及宇宙审查制度与WGC之间的推测关系，它们永远不会形成裸奇点。这种过度充电的壳层存在的一个有趣的结果是，由于雷格-惠勒-泽里利势的特殊形式，引力模式可能会形成束缚态。这可能会导致重力陷阱关闭接近过度充电的炮弹表面。