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Dynamical Emergence of Universal Horizons during the formation of Black Holes

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In many theories with fundamental preferred frame, such as Einstein-Aether or Gravitational Aether theories, K-essence, Cuscuton theory, Shape Dynamics, or (non-projectable) Horava-Lifshitz gravity, the low energy theory contains a fluid with superluminal or incompressible excitations. In this talk, I study the formation of black holes in the presence of such a fluid. In particular, I focus on the incompressible limit of the fluid (or Constant Mean Curvature foliation) in the space-time of a spherically collapsing shell within an asymptotically cosmological space-time. In this case, I show that an observer inside 3/4 of the Schwarzschild radius cannot send a signal outside, after a stage in collapse, even using signals that propagate infinitely fast in the preferred frame. This confirms the dynamical emergence of universal horizons that have been previously found in static solutions [arXiv:1110.2195, arXiv:1104.2889, arXiv:1212.1334].