Anti de Sitter black holes and branes in dynamical Chern-Simons gravity: perturbations, stability and the hydrodynamic modes

Abstract: Dynamical Chern-Simons (DCS) theory is an extension of General Relativity in which the gravitational field is coupled to a scalar field through a parity violating term. We study perturbations of anti-de Sitter black holes and branes in such a theory, and show that the relevant equations reduce to a set of coupled ODEs which can be solved efficiently through a series expansion. We prove numerically that black holes and branes in DCS gravity are stable against gravitational and scalar perturbations in the entire parameter space. Furthermore, by applying the AdS/CFT duality, we relate black hole perturbations to hydrodynamic quantities in the dual field theory, which is a (2+1)-dimensional isotropic fluid with broken spatial parity. The Chern-Simons term does not affect the entropy to viscosity ratio and the relaxation time, but instead quantities that enter the shear mode at order q^4 in the small momentum limit, for example the Hall viscosity and other quantities related to second and third order hydrodynamics. We provide explicit corrections to the gravitational hydrodynamic mode to first relevant order in the couplings.