Membrane paradigm of black holes in Chern-Simons modified gravity

The membrane paradigm of black hole is studied in the Chern-Simons modified gravity. Derived with the action principle a la Parikh-Wilczek, the stress tensor of membrane manifests a rich structure arising from the Chern-Simons term. The membrane stress tensor, if related to the bulk stress tensor in a special form, obeys the low-dimensional fluid continuity equation and the Navier-Stokes equation. This paradigm is applied to spherically symmetric static geometries, and in particular, the Schwarzschild black hole, which is a solution of a large class of dynamical Chern-Simons gravity.