A possible violation of the weak gravity conjecture (WGC) by cosmic censorship is one of the major challenges in the field of general relativity. The cosmic censorship is a fundamental principle that ensures the consistency of the theory of gravity. According to this principle, a charged black hole in four dimensions cannot violate the weak cosmic censorship conjecture (WCCC) under normal conditions. However, in this paper, we explore the possibility of reconciling the WGC and the WCCC by considering Reissner-Nordström (R-N) black holes embedded in perfect fluid dark matter (PFDM) in asymptotically flat spacetimes. These two conjectures are seemingly unrelated, but a recent proposal suggested that they are connected surprisingly. In particular, We argue a promising class of valid counterexamples to the WCCC in the four-dimensional Einstein-Maxwell theory, considering a charged black hole when WGC is present. We demonstrate that by imposing certain constraints on the parameters of the metric, the WGC and the WCCC can be compatible. Furthermore, we investigate the properties of the charged black hole in the presence of PFDM for and present some intriguing figures to test the validity of the WGC and the WCCC simultaneously. When PFDM is absent (), the RN black hole either has two event horizons if or none if . The second scenario results in a naked singularity, which contradicts the WCCC. But when PFDM is present (), the RN black hole has event horizons with regard to Q and M. This implies that the singularity is always covered, and the WGC and the WCCC are fulfilled. Furthermore, we demonstrate that there is a critical value of , called , that makes the RN black hole extremal when . In this situation, the black hole has an event horizon, and the WGC and the WCCC are still fulfilled. We infer that PFDM can make the WGC and the WCCC compatible with the RN black hole and that the WGC and the WCCC agree with each other when PFDM is present.

中文翻译：

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被完美流体暗物质包围的赖斯纳-诺德斯特伦黑洞：同时测试弱引力猜想和弱宇宙审查猜想的可行性


宇宙审查制度可能违反弱引力猜想（WGC），这是广义相对论领域的主要挑战之一。宇宙审查是确保引力理论一致性的基本原则。根据这一原理，四维带电黑洞在正常情况下不能违反弱宇宙审查猜想（WCCC）。然而，在本文中，我们通过考虑渐进平坦时空中完美流体暗物质（PFDM）中嵌入的赖斯纳-诺德斯特伦（R-N）黑洞来探索调和 WGC 和 WCCC 的可能性。这两个猜想看似无关，但最近的一项提议表明它们之间有着惊人的联系。特别是，考虑到 WGC 存在时的带电黑洞，我们提出了四维爱因斯坦-麦克斯韦理论中 WCCC 的一类有希望的有效反例。我们证明，通过对度量参数施加某些约束，WGC 和 WCCC 可以兼容。此外，我们研究了 PFDM 存在下带电黑洞的特性，并提供了一些有趣的数据来同时测试 WGC 和 WCCC 的有效性。当 PFDM 不存在 () 时，RN 黑洞要么有两个事件视界，要么没有。第二种情况会导致裸奇点，这与 WCCC 相矛盾。但当 PFDM 存在时 ()，RN 黑洞具有关于 Q 和 M 的事件视界。这意味着奇点总是被覆盖，并且满足 WGC 和 WCCC。此外，我们证明了存在一个称为 的临界值，当 时，该值使 RN 黑洞达到极值。 在这种情况下，黑洞具有事件视界，WGC和WCCC仍然满足。我们推断PFDM可以使WGC和WCCC与RN黑洞兼容，并且当PFDM存在时WGC和WCCC彼此一致。