Thermodynamics and phase transitions of charged-AdS black holes in dRGT massive gravity with nonlinear electrodynamics

Abstract

Investigating black holes in modified theories of gravity offers fertile ground for exploring phenomena beyond the scope of general relativity. We investigate a novel class of charged anti-de Sitter (AdS) black holes within the ghost-free de Rham-Gabadadze-Tolley (dRGT) massive gravity, minimally coupled to an exponential form of nonlinear electrodynamics (NED). The NED sector is modelled by an exponential electrodynamics Lagrangian, which leads to singular black hole geometries in contrast to many regular configurations known in other NED models. In turn, we systematically investigate the thermodynamic properties and phase structure of the obtained black holes. The results show that the system has a rich thermodynamic structure. For different values of the magnetic charge $q$, the black hole can exhibit several types of phase transitions. These include van der Waals-like first-order phase transitions, second-order critical behavior, and a reentrant phase transition between small and large black holes without extending the phase space ($Λ=$constant). Our study enhances the understanding of AdS black holes in ghost-free massive gravity, providing further insights into the interplay between graviton mass and NED. The results highlight how the combined effects of graviton mass and electromagnetic nonlinearity can yield a rich and complex thermodynamic phase space, offering further insights relevant to the gauge/gravity duality and the ongoing search for observational signatures of modified gravity.

Figures (7)

• Figure 1: Metric function $F(r)$ vs $r$ for different $q$ with $\gamma = -1$, $\zeta = 2.9$, $k = 0.1$. Curves: $q = 0$ (black dashed), $q = 0.2$ (blue), $q = q_E = 0.466$ (red), $q = 0.7$ (green). The critical charge $q_E$ corresponds to the extremal black hole.
• Figure 2: Metric function $F(r)$ vs $r$ for different $k$ with $\gamma = -1$, $\zeta = 2.9$, $q = 0.466$. Curves: $k = 0.05$ (red), $k = 0.1$ (black dashed), $k = 0.5$ (blue). The extremal case corresponds to $k = 0.1$.
• Figure 3: Hawking temperature $T_+$ vs horizon radius $r_+$ for different $q$ with $k = 0.1$, $\alpha_3 = 0.1$, $\alpha_4 = 0.2$. The curves show multiple branches separated by temperature extrema. Critical charges $q_{c1}$ and $q_{c2}$ mark the merging of extrema.
• Figure 4: Critical charge $q_c$, horizon radius $r_c$, and temperature $T_c$ vs nonlinear parameter $k$ for $\alpha_3 = 0.1$, $\alpha_4 = 0.2$. Red and green curves correspond to first and second critical points.
• Figure 5: Specific heat $C_q$ vs horizon radius $r_+$ for different $q$ with $k = 0.1$, $\alpha_3 = 0.1$, $\alpha_4 = 0.2$. The positive (negative) $C_q$ indicates local stability (instability). Divergences mark phase transitions.