We construct a generalized Smarr formula which could provide a thermodynamic route to derive the covariant field equation of general theories of gravity in dynamic spacetimes. Combining some thermodynamic variables and a new chemical potential conjug
ated to the number of degree of freedom on the holographic screen, we find a universal Cardy-Verlinde formula and give its braneworld interpretation. We demonstrate that the associated AdS-Bekenstein bound is tighten than the previous expression for multi-charge black holes in the gauged supergravities. The Cardy-Verlinde formula and the AdS-Bekenstein bound are derived from the thermodynamics of bulk trapping horizons, which strongly suggests the underlying holographic duality between dynamical bulk spacetime and boundary field theory.
Recently, it has been shown that if we consider the higher derivative correction, the viscosity bound conjectured to be $eta/s=1/4pi$ is violated and so is the causality. In this paper, we consider medium effect and the higher derivative correction s
imultaneously by adding charge and Gauss-Bonnet terms. We find that the viscosity bound violation is not changed by the charge. However, we find that two effects together create another instability for large momentum regime. We argue the presence of tachyonic modes and show it numerically. The stability of the black brane requires the Gauss-Bonnet coupling constant $lambda$($=2alpha/l^2$) to be smaller than 1/24. We draw a phase diagram relevant to the instability in charge-coupling space.
We study the transport coefficients of Quark-Gluon-Plasma in finite temperature and finite baryon density. We use AdS/QCD of charged AdS black hole background with bulk-filling branes identifying the U(1) charge as the baryon number. We calculate the
diffusion constant, the shear viscosity and the thermal conductivity to plot their density and temperature dependences. Hydrodynamic relations between those are shown to hold exactly. The diffusion constant and the shear viscosity are decreasing as a function of density for fixed total energy. For fixed temperature, the fluid becomes less diffusible and more viscous for larger baryon density.
