The thermodynamics and phase transitions of charged RN-AdS and rotating Kerr-AdS black holes in a generalized Randall-Sundrum braneworld are investigated in the framework of thermodynamic geometry. A detailed analysis of the thermodynamics, stability
and phase structures in the canonical and the grand canonical ensembles for these AdS braneworld black holes are described. The thermodynamic curvatures for both these AdS braneworld black holes are computed and studied as a function of the thermodynamic variables. Through this analysis we illustrate an interesting dependence of the phase structures on the braneworld parameter for these black holes.
We obtain (2+1) dimensional p-wave holographic superconductors from charged Born-Infeld black holes in the presence of massive charged vector fields in a bulk $AdS_4$ Einstein-Born-Infeld theory through the $AdS_4$-$CFT_3$ correspondence. Below a cer
tain critical transition temperature the charged black hole develops vector hair that corresponds to charged vector condensate in the strongly coupled (2+1) dimensional boundary field theory that breaks both the $U(1)$ symmetry as well as the rotational invariance. The holographic free energy is computed for the boundary field theory which shows that the vector order parameter exhibits a rich phase structure involving zeroth order, first order, second order and retrograde phase transitions for different values of the backreaction and the Born-Infeld parameters. We numerically compute the ac conductivity for the p-wave superconducting phase of the strongly coupled (2+1) dimensional boundary field theory which also depends on the relative values of the parameters in the theory.
We investigate phase transitions and critical phenomena of four dimensional dyonic charged AdS black holes in the framework of thermodynamic geometry. In a mixed canonical grand canonical ensemble with a fixed electric charge and varying magnetic cha
rge these black holes exhibit liquid gas like first order phase transition culminating in a second order critical point similar to the Van der Waals gas. We show that the thermodynamic scalar curvature R for these black holes follow our proposed geometrical characterization of the R-crossing Method for the first order liquid gas like phase transition and exhibits a divergence at the second order critical point. The pattern of R crossing and divergence exactly corresponds to those of a Van der Waals gas described by us in an earlier work.
We consider a system of two massive, mutually interacting probe real scalar fields, in zero temperature holographic backgrounds. The system does not have any continuous symmetry. For a suitable range of the interaction parameters adhering to the inte
raction potential between the bulk scalars, we have shown that as one turns on the source for one scalar field, the system may go through a second order quantum critical phase transition across which the second scalar field forms a condensate. We have looked at the resulting phase diagram and numerically computed the condensate. We have also investigated our system in two different backgrounds: $AdS_4$ and $AdS$ soliton, and got similar phase structure.
