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### A proof of the instability of AdS spacetime for the Einsteinâ€“massless Vlasov system

**PDE and Applied Math Seminar**

Speaker: | Georgios Moschidis, UC Berkeley |

Related Webpage: | https://web.math.princeton.edu/~gm6/ |

Location: | 2112 MSB |

Start time: | Fri, Feb 15 2019, 4:10PM |

The AdS instability conjecture is a conjecture about the

initial-boundary value problem in general relativity. It states that

there exist arbitrarily small perturbations to the initial data of AdS

spacetime which, under evolution by the vacuum Einstein equations with

reflecting boundary conditions on conformal infinity, lead to the

formation of black holes after sufficiently long time. In recent

years, a vast amount of numerical and heuristic works have been

dedicated to the study of the instability of AdS, focusing mainly on

the simpler setting of the spherically symmetric Einstein--scalar

field system.

In this talk, I will present a rigorous proof of the AdS

instability conjecture in the setting of the spherically symmetric

Einstein--massless Vlasov system. The construction of the unstable

family of initial data will require working in a low regularity

setting, carefully designing a family of initial configurations of

localised Vlasov beams and estimating the exchange of energy taking

place between interacting beams over long period of times. If time

permits, I will briefly discuss how the main ideas of the proof can be

extended to more general matter fields.