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Dynamical Chern-Simons (DCS) theory is an extension of General Relativity inwhich the gravitational field is coupled to a scalar field through a parityviolating term. We study perturbations of anti-de Sitter black holes and branesin such a theory, and show that the relevant equations reduce to a set ofcoupled ODEs which can be solved efficiently through a series expansion. Weprove numerically that black holes and branes in DCS gravity are stable againstgravitational and scalar perturbations in the entire parameter space.Furthermore, by applying the AdS/CFT duality, we relate black holeperturbations to hydrodynamic quantities in the dual field theory, which is a(2+1)-dimensional isotropic fluid with broken spatial parity. The Chern-Simonsterm 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 smallmomentum limit, for example the Hall viscosity and other quantities related tosecond and third order hydrodynamics. We provide explicit corrections to thegravitational hydrodynamic mode to first relevant order in the couplings.

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