Van der Waals like behavior of topological AdS black holes in massive gravity

Motivated by recent developments in black hole thermodynamics, we investigate van der Waals phase transitions of charged black holes in massive gravity. We find that massive gravity theories can exhibit strikingly different thermodynamic behavior compared to that of Einstein gravity, and that the mass of the graviton can generate a range of new phase transitions for topological black holes that are otherwise forbidden.

Figure 1

$\psi (r)$ versus $r$ for $\mathrm{\Lambda }=-1$, $d=4$, $q=1.7$, $c=1.00$, $c_1=-2.00$, $c_2=3.18$, $c_3=4.00$ and $m_0=30$. Left panel: $m=2.1$, $k=-1$ (dotted line), $k=0$ (continuous line) and $k=1$ (dashed line). Right panel: $k=-1$, $m=2.16$ (dotted line), $m=2.12$ (continuous line) and $m=2.07$ (dashed line).

Figure 2

$P-r_{+}$ (left panel) and $G-T$ (right panel) diagrams for $d=4$, $q=m=c=c_1=c_3=1$ and $c_2=10$. Left panel $T=T_c$, right panel $P=0.5P_c$: $k=-1$ (continuous line), $k=0$ (dotted line) and $k=1$ (dashed line).

Figure 3

$P-r_{+}$ (left panel) and $G-T$ (right panel) diagrams for $d=4$, $q=m=c=c_1=1$, $k=-1$ and $c_2=10$. Left panel $T=T_c$, right panel $P=0.5P_c$: $c_3=0$ (continuous line), $c_3=1$ (dotted line) and $c_3=2$ (dashed line).