Towards Fluid Instabilities of Stationary Non-Killing Horizons

Flowing black holes are asymptotically locally AdS spacetimes that are stationary but have non-Killing horizons. Holographically, they are dual to a steady-state heat flow in the boundary field theory. We investigate the stability of these black holes in the limit in which they are well-described by the relativistic conformal Navier-Stokes equations. More precisely, we study the quasi-normal modes of the linearized ideal fluid equations. Though we find no unstable modes, there are an infinite number at finite transverse momentum which are arbitrarily long-lived. This suggests the possibility that either non-modal effects or nonlinear interactions between these modes can give rise to new types of gravitational instabilities.