AdS/CFT and the Weak Cosmic Censorship Conjecture

由于罗杰·彭罗斯（Roger Penrose）和斯蒂芬·霍金（Stephen Hawking）在70年代的开创性工作，我们知道广义相对论允许从一般初始数据形成奇点。然而，对于这些奇点是否可以被遥远的观察者观察到，或者它们是否一定被事件视界所覆盖，人们知之甚少。这是弱宇宙审查猜想（WCCC）的内容，该猜想断言事件视界必然会掩盖奇点。具有渐近平坦边界条件的四维时空WCCC问题目前已经通过了无数种情形，但仍然是数学广义相对论中最突出的问题。然而，在高于或等于给定的时空维度中，已经发现了一种违反WCCC的机制：每当黑洞视界发展出很大的梯度，并且没有电场时，它们就会像流体柱一样试图破裂。这种现象被称为格雷戈里-拉弗拉姆机制，以两位最先设想这种现象的物理学家的名字命名。一个看似无关的话题是规范引力二象性，它假设在某些背景下的弦理论和生活在较低维度的某些量子场论之间存在完全等价。虽然引力在二象性的弦理论方面是动态的，但它在量子场论方面完全不存在。由于弦理论只能在十维（或十一维）中一致地表述，有人可能会问上面简要提到的格雷戈里-拉弗拉姆机制是否可以发挥作用。事实上，有一个长期的场景似乎是这样的，但到目前为止，所有从量子场论和弦理论方面研究这一现象的尝试都没有解释弦理论效应如何或是否确实解决了奇点。这个项目的目的是第一次用数值模拟，一个可以观察到对偶的弦理论方面的格雷戈里-拉弗拉姆机制的例子，看看这种现象的量子场论特征是什么。希望这种理解将使我们能够引导我们的知识，并提供纯粹根据量子场论数据的奇点分辨率。

Due to the seminal work of Roger Penrose and Stephen Hawking in the seventies, we know that general relativity allows for the formation of singularities from generic initial data. However, little is known about whether these singularities can be observed by distant observers, or whether they are necessarily covered by an event horizon. This is the content of the Weak Cosmic Censorship Conjecture (WCCC), which asserts that event horizons will necessarily cloak singularities. The WCCC in four spacetime dimensions with asymptotically flat boundary conditions has now passed a myriad of scenarios, but remains the most outstanding problem in mathematical general relativity. In spacetime dimensions above or equal to give, however, a mechanism for violations of the WCCC has been found: whenever black hole horizons develop large gradients, and electric fields are absent, they will attempt to break just like a column of fluid. This goes by the name of the Gregory-Laflamme mechanism, named after the two physicists that first envisage this phenomenon. A seemingly unrelated topic is the gauge gravity duality, which posits a complete equivalence between string theory on certain backgrounds and certain quantum field theories living in lower dimensions. While the gravity is dynamical on the string theory side of the duality, it is absent entirely on the quantum field theory side. Since string theory is only consistently formulated in ten (or eleven) dimensions, one might ask whether the Gregory-Laflamme mechanism briefly mentioned above can play a role. Indeed, there is a longstanding scenario where this appears to be the case, but so far all attempts to study this phenomenon from both the quantum field theory side and string theory side have fallen short of an explanation for how or if string theory effects do resolve the singularity. The aim of this project is to simulate numerically, for the very first time, an instance where one can observe the Gregory-Laflamme mechanism on the string theory side of the duality and see what the quantum field theory signature of this phenomenon is. Hopefully, this understanding will allows us to bootstrap our knowledge and provide a singularity resolution purely in terms of quantum field theory data.