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Abstract The verification of the second law of black hole mechanics and the WCCC in the context of enthalpy as mass of the black hole and its related thermodynamic properties has not been tested through a vast number of literature in the recent past. Such studies are of great physical importance as they provide us with a large number of information regarding the thermodynamics and the dynamics of AdS black hole systems. We invest the prior limited surveys of such analysis to investigate the WCCC for the D- dimensional asymptotically AdS-charged black holes characterized by its mass (M), electric charge (Q), and AdS radius (l) under the absorption of scalar particles of charge q. We examine the WCCC by analyzing the energy-momentum condition of the electrically charged particles as absorbed by the black holes. We prove that the conjecture is well verified irrespective of whether the initial black hole configurations are extremal or non-extremal by changing its charge, the AdS radius, and their variations. We show that the first law and the WCCC are valid for all spacetime dimensions (D) independent of the choice of the parameters characterizing the black holes. But to verify the second law in the extremal and non- extremal configurations one has to be very cautious as it gets strongly affected by the choices of the values of the black hole parameters and their variations. In other words, we use charged particle dynamics as described by the Hamilton-Jacobi equation to obtain the energy-momentum relation as the charged particle dropped into the higher dimensional charged AdS black hole and verify the thermodynamic laws when the scalar charged particle gets absorbed by the black holes and correspondingly the black hole neutralization in different manners. Additionally, we further probe the validity of WCCC in such a black hole background. In the context of the extended phase space, taking the grand canonical potential into account allow us to obtain the missing information about the variation of the cosmological constant necessary to construct the extended phase space, namely the notion of the black hole pressure, and which is absent in the previous literature so far.

We investigate numerically fR gravity effects on certain AdS/CFT tools including holographic entanglement entropy and two-point correlation functions for a charged single accelerated Anti-de Sitter black hole in four dimensions. We find that both holographic entanglement entropy and two-point correlation functions decrease by increasing the acceleration parameter A, matching perfectly with literature. Taking into account the fR gravity parameter η, the decreasing scheme of the holographic quantities persist. However, we observe a transition-like point where the behavior of the holographic tools changes. Two regions meeting at such a transit-like point are shown up. In such a nomination, the first one is associated with slow accelerating black holes while the second one corresponds to a fast accelerating solution. In the first region, the holographic entanglement entropy and two-point correlation functions decrease by increasing the η parameter. However, the behavioral situation is reversed in the second one. Moreover, a cross-comparison between the entropy and the holographic entanglement entropy is presented, providing another counterexample showing that such two quantities do not exhibit similar behaviors.

In this paper, we study Joule-Thomson expansion for charged AdS black holes in \(f(R)\) gravity. We obtain the inversion temperatures as well as inversion curves, and investigate similarities and differences between van der Waals fluids and charged AdS black holes in \(f(R)\) gravity for this expansion. In addition, we determine the position of the inversion point versus different values of the mass \(M\), the charge \(Q\) and the parameter \(b\) for such black hole. At this point, the Joule-Thomson coefficient \(\mu\) vanishes, an import feature that we used to obtain the cooling-heating regions by scrutinizing the sign of the \(\mu\) quantity.