  We discuss the phase transitions between three states of a plasma fluid
(plasma ball, uniform plasma tube, and non-uniform plasma tube), which are dual
to the corresponding finite energy black objects (black hole, uniform black
string, and non-uniform black string) localized in an asymptotically locally
AdS space. Adopting the equation of state for the fluid obtained by the
Scherk-Schwarz compactification of a conformal field theory, we obtain
axisymmetric static equilibrium states of the plasma fluid and draw the phase
diagrams with their thermodynamical quantities. By use of the fluid/gravity
correspondence, we predict the phase diagrams of the AdS black holes and
strings on the gravity side. The thermodynamic phase diagrams of the AdS black
holes and strings show many similarities to those of the black hole-black
string system in a Kaluza-Klein vacuum. For instance, the critical dimension
for the smooth transition from the uniform to non-uniform strings is the same
as that in the Kaluza-Klein vacuum in the canonical ensemble. The analysis in
this paper may provide a holographic understanding of the relation between the
Rayleigh-Plateau and Gregory-Laflamme instabilities via the fluid/gravity
correspondence.
