A Variational Principle for Asymptotically Randall-Sundrum Black Holes
  We prove the following variational principle for asymptotically Randall-Sundrum (RS) black holes, based on the first law of black hole mechanics: Instantaneously static initial data that extremizes the mass yields a static black hole, for variations at fixed apparent horizon area, AdS curvature length, cosmological constant, brane tensions, and RS brane warp factors. This variational principle is valid with either two branes (RS1) or one brane (RS2), and is applicable to variational trial solutions. 
Scott Fraser, Douglas M. Eardley
gr-qc hep-th