Joule-Thomson expansion for quantum corrected AdS-Reissner-Nördstrom black holes in Kiselev spacetime with Barrow fractal entropy

TL;DR

This work investigates how quantum corrections in black-hole geometry ($a$) versus fractal entropy corrections ($\Delta$) influence the Joule–Thomson expansion for AdS-Reissner–Nordström black holes in Kiselev spacetime. Analytically, it derives Barrow-entropy–modified thermodynamics, including the horizon-based mass $M$, entropy $S=(\pi r_+^2)^{1+\Delta/2}$, and temperature $T$, and identifies the inversion-temperature condition $T_i=V(\partial T/\partial V)_P$, with a numerically solvable relation between horizon radius $r_+$ and inversion pressure $P_i$. Numerically, increasing $\Delta$ lowers $T_i$ at fixed $P$ and raises the inversion pressure, while metric correction $a$ shifts the zero-point structure and modulates the curves alongside the Kiselev fluid parameters $\omega$, $c$, and $Q$. The results illuminate how fractal entropy and geometric quantum corrections imprint distinct thermodynamic fingerprints on black-hole JT flows, with potential implications for quantum gravity phenomenology and black-hole microstate analyses.

Abstract

How can we detect the difference in the effects of the quantum corrections included in the metric of a spacetime and the quantum corrections included in the entropy of such a system? Recently, J. Barrow designed an expression based directly on black hole (BH) entropy of Bekenstein-Hawking where the geometry of the event horizon can also have an intricate, non smooth, structure, a fractal geometry. These fractal features are represented by a numerical constant parameter, the fractal parameter (FP). Since then, several interesting issues have been explored in the literature. In this work, we investigate the inversion temperature connected to the Joule-Thomson expansion from the thermodynamics of AdS-Reissner-Nördstrom BH by using the Barrow entropy equation where the FP has several values within a certain validity interval. We include quantum corrections in a cosmological fluid that can describe phantom dark matter or quintessence, both in a Kiselev scenario. The description of such physical systems also involves numerical solutions concerning the FP. The results are shown by temperature-pressure curves for multiple values of the parameters of the system used here. In conclusion of our analysis, we also show isenthalpic curves corresponding to fixed-mass BH processes, and we respond numerically to the question made in the first line of this abstract.

Figures (10)

• Figure 1: Inversion temperature as a function of the pressure for fixed $\omega = -1.0$, $c = 0.1$, $a = 0.1$, $Q = 1.0$, and the corrections to entropy: $\Delta = 0$ (blue line), $\Delta = 1/4$ (red line), $\Delta = 1/2$ (black line), $\Delta= 3/4$ (cyan line) and $\Delta=1$ (green line). The upper panels show small and large behaviors of $T_i \times P$, while the lower panels depict different ranges of these functions, with the purpose of showing the intercept points of these curves for different values of $\Delta$.
• Figure 2: Inversion temperature as a function of the pressure for fixed $\omega = -1.0$, $c = 0.1$, $a = 0.1$, small range, and the values for charge: $Q = 1.0$ (green line), $Q = 2.0$ (red line), $Q = 3.0$ (black line) and $Q= 6.0$ (blue line). Solid lines are obtained from $\Delta=0$, dotted lines from $\Delta=1/2$ and dashed lines from $\Delta=1$. Left panel: small range. Right panel: large range.
• Figure 3: Inversion temperature as a function of the pressure for fixed $Q = 2.5$, $c = 0.1$, $a = 0.1$, varying $\omega$: $\omega = -1.6$ (green line), $\omega = -2/3$ (red line), $\omega = -1$ (black line) and $\omega = -4/3$ (blue line). Solid lines are obtained from $\Delta=0$, dotted lines from $\Delta=1/2$ and dashed lines from $\Delta=1$. Left panel: small range. Right panel: large range.
• Figure 4: Inversion temperature as a function of the pressure for fixed $\omega = -1.0$, $c = 0.1$, $Q = 1.0$, and the values for the quantum corrections: $a = 0.1$ (blue line), $a = 0.3$ (red line), $a = 0.4$ (black line). Solid lines are obtained with $\Delta=0$, dotted with $\Delta=1/2$, and dashed lines with $\Delta=1$.
• Figure 5: Inversion temperature as a function of the pressure for fixed $\omega = -1/6$, $a = 0.1$, $Q = 1.0$, varying $c$: $c = 0.01$ (red line), $c = 0.10$ (blue line), $c = 1.00$ (black line). Solid lines are obtained with $\Delta=0$, dotted lines from $\Delta=1/2$ and dashed lines from $\Delta=1$. Left panel: small range. Right panel: large range.