Title: Gravity in a conformal box
Abstract: We investigate gravitational dynamics in the presence of finite timelike boundaries with conformal boundary conditions. We focus on the limit in which the conformal boundary approaches a black hole or cosmological horizon. In this regime, potentially exponentially growing perturbations are attenuated, and we find a hierarchy of modes localized near the conformal boundary. In particular, we uncover sound and shear modes that admit an interpretation in terms of a conformal fluid with shear-viscosity-to-entropy-density ratio \eta/s=1/(4\pi). For the AdS4 black brane, we track these modes numerically as the boundary is moved from the near-horizon region towards the asymptotic AdS boundary, and find that they continuously connect to the hydrodynamic sound and shear modes of the fluid/gravity correspondence.