We investigate the phase structure of a charged AdS dilaton black hole in the extended phase space which takes the cosmological constant, i.e. the AdS-Λ parameter as pressures. Through both thermal ensemble and quasinormal mode analysis, we find that stable phase of the black hole with non-trivial dilaton profiles always exists for both large and small couplings when the AdS-Λ is considered dynamical degrees of freedom. This forms a somewhat contrast with previous works which does not do so. Our results provide new examples for the parallelism or equivalences between thermal ensemble methods and dynamic perturbation analysis for black hole phase structures.

Using ideas of cosmological perturbation theories, we make general linear stability analysis of dynamic thin-shell wormholes constructed by cutting-and-pasting two buildingblock spacetimes at arbitrary joining shell radius. We observed that in appropriate parameter choices, dynamical thin shell wormholes following from such a cut-and-paste procedure can be kept stable during the whole evolution process towards the final extremal point on which the joining shell radius reaches on static values. Our work forms a valuable complementarity to previous analysis basing on virtual spherical perturbations around the born-static configuration of the wormholes.

In the background of a charged AdS dilaton black hole, we investigate the movement of a selfgraviting 3-brane and relevant holographic effects as the brane move close to the AdS boundary. The induced metric on brane corresponds to an exact FLRW geometry, while the evolution of brane is determined by Israel junction condition and the effective Einstein field equation on brane together. When the brane approaches the AdS boundary, AdS/CFT correspondence implies that a radiation dominated FLRW-universe (P = 1 3 ρ) should be given. According to the holographic renormalization procedure, we involve an appropriate surface counterterm into the gravitational action for achieving P = 1 3 ρ on brane. This surface counterterm also plays a important role in caculating the mass of charged AdS dilaton black hole. Finally, we obtain the thermodynamic quantities and give an extend Cardy-Verlinde formula on brane.

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