AdS/CFT and the Weak Cosmic Censorship Conjecture

点击翻译按钮获取中文摘要

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.