Critical behavior of charged Gauss-Bonnet-AdS black holes in the grand canonical ensemble

We study the thermodynamics in the grand canonical ensemble of $D$-dimensional charged Gauss-Bonnet-AdS black holes in the extended phase space. We find that the usual small-large black hole phase transition, which exhibits analogy with the van der Waals liquid-gas system, holds in five-dimensional spherical charged Gauss-Bonnet-AdS black holes when its potential is fixed within the range $0<\mathrm{\Phi }<\frac{\sqrt{3}\pi }{4}$. For the other higher dimensional and topological charged Gauss-Bonnet-AdS black holes, there is no such phase transition. In the limiting case, Reissner-Nordstrom AdS black holes, with vanishing Gauss-Bonnet parameter, there is no critical behavior in the grand canonical ensemble. This result holds independent of the spacetime dimensions and topologies. We also examine the behavior of physical quantities in the vicinity of the critical point in the five-dimensional spherical charged Gauss-Bonnet-AdS black holes.

Figure 1

The $P-r_{+}$ diagram of spherical GB-AdS black holes in the grand canonical ensemble for $\mathrm{\Phi }=1$, ${\tilde{\alpha }}_{GB}=0.01$ and $D=5$.

Figure 2

The Gibbs free energy $G$ of spherical charged GB-AdS black holes and coexistence line of small-large black holes phase transition in the grand canonical ensemble for $\mathrm{\Phi }=1$, ${\tilde{\alpha }}_{GB}=0.01$ and $D=5$.