AdS Length corrected Thermodynamics of a Black Hole in a Cloud of Strings and Perfect Fluid Dark Matter

TL;DR

This work analyzes a Reissner-Nordström–AdS black hole embedded in a cloud of strings and perfect fluid dark matter, focusing on the impact of a small perturbation to the AdS length scale on its thermodynamics in the extended phase space. The authors derive the uncorrected thermodynamic quantities, including entropy $S_0 = \pi r_+^2$, from the RN-AdS-CoS-PFDM solution with parameters $a$ and $\lambda$, and present expressions for $M$, $T_H$, $H_0$, $F_0$, $P_0$, $U_0$, $G_0$, and $C_0$. They then implement the correction by $l \to l/\sqrt{1+\epsilon}$, obtaining corrected $S_c$, $H_c$, $F_c$, $P_c$, $U_c$, $G_c$, and $C_c$, and find that $\epsilon>0$ enhances most quantities while $\epsilon<0$ can yield negative or divergent behavior, including a Davies-type phase transition near $r_+ \approx 0.75$. Overall, the results highlight the nontrivial interplay between exotic matter fields (CoS, PFDM) and geometric AdS-length corrections in shaping black hole thermodynamics and stability.

Abstract

We investigate the thermodynamic characteristics of the Reisner-Nordstrom black hole in AdS spacetime with a cloud of strinsg and perfect fluid dark matter background, employing a minor correction to the AdS radius. Although the entropy remains unaltered, enthalpy, free energies, pressure, internal energy, and specific heat exhibit considerable modifications. These quantities get enhanced generally by the positive correction ($ε> 0$) to the AdS scale and lead to faster growth/ slower decay with increase in horizon radius. The opposite effect is reflected by negative corrections ($ε< 0$), which sometimes result in negative or divergent behaviour. We find an interconnection between the combined effect of exotic matter fields and geometric corrections on black hole thermodynamics and thermodynamic stability.

Figures (6)

• Figure 1: Enthalpy $H_c$ v/s horizon radius $r_+$ with different values of $\epsilon$. The curves show the behavior for $\epsilon = 0$ (uncorrected), $\epsilon > 0$, and $\epsilon < 0$.
• Figure 2: Free energy $F_c$ v/s horizon radius $r_+$ with different values of $\epsilon$. The curves show the behavior for $\epsilon = 0$ (uncorrected), $\epsilon > 0$, and $\epsilon < 0$.
• Figure 3: Pressure $P_c$ v/s the horizon radius $r_+$ with different values of $\epsilon$. The curves show the behavior for $\epsilon = 0$ (uncorrected), $\epsilon > 0$, and $\epsilon < 0$.
• Figure 4: Corrected Internal energy $U_c$ v/s horizon radius $r_+$ with different values of $\epsilon$. The curves show the behavior for $\epsilon = 0$ (uncorrected), $\epsilon > 0$, and $\epsilon < 0$.
• Figure 5: Corrected Gibbs free energy $G_c$ v/s horizon radius $r_+$ with different values of $\epsilon$. The curves show the behavior for $\epsilon = 0$ (uncorrected), $\epsilon > 0$, and $\epsilon < 0$.