Charged AdS black holes in presence of string cloud and Cardy-Verlinde formula

In this study, charged AdS black holes with a string cloud are taken into consideration. We identify three distinct black hole solutions within a specific temperature range, which subsequently merge into a single black hole beyond this range in the case of spherical space with low chemical potential and string density. However, in the case of large chemical potential and string density, only one black hole solution exists for all temperatures. Notably, we observe that for flat and hyperbolic space, there is only one black hole solution irrespective of the chemical potential and string density. By subtracting the contribution of the extremal black hole from the on-shell Euclidean action, the thermodynamical quantities associated with these black holes are calculated. We also investigate the stability of these black holes and find that medium-sized black hole is unstable. In the dual boundary theory side we verify the existence of bound state of quark-antiquark pair. Finally, we establish the Cardy-Verlinde formula for the boundary theory and we observed an additional energy term arising because of the presence of string cloud.