Thermodynamics, photon sphere and thermodynamic geometry of Ayón-Beato-García Spacetime

TL;DR

The paper investigates the ABG-AdS black hole in extended thermodynamics, linking its van der Waals–like phase structure to photon-sphere properties and thermodynamic geometry. It shows that the photon-sphere radius and minimum impact parameter behave as order parameters for the SBH–LBH transition with a critical exponent of $1/2$, and demonstrates a universal scaling in the near-critical regime. The Ruppeiner geometry analysis reveals distinct microstructures: LBH corresponds to attractive (bosonic-like) interactions, while SBH exhibits both attractive and repulsive (anyon-like) interactions, with a universal near-critical exponent $p\approx 2$ and $R_N(1-\tilde{T})^2\to -1/8$. Overall, the work deepens the connections between gravity, black hole thermodynamics, photon trajectories, and microscopic interactions in regular black hole spacetimes.

Abstract

We study the thermodynamics of the Ayón-Beato-García black hole and the relationship between photon orbits and the thermodynamic phase transitions of the black hole in AdS spacetime. We then examine the interactions between the microstructures of the black hole using Ruppeiner geometry. The radius of the photon orbit and the minimum impact parameter behave non-monotonically below the critical point, mimicking the behaviour of Hawking temperature and pressure in extended thermodynamics. Their changes during the large black hole--small black hole phase transition serve as the order parameter, possessing a critical exponent of $1/2$. The results demonstrate that the gravity and thermodynamics of the Ayón-Beato-García black hole are closely related. Furthermore, we explore the thermodynamic geometry, which provides insight into the microstructure interactions of the black hole. We find that the large black hole phase is analogous to a bosonic gas with a dominant attractive interaction, while the small black hole phase behaves like an anyonic gas with both attractive and repulsive interactions.

Figures (12)

• Figure 1: (a) Reduced pressure ($\tilde{P}$) versus reduced volume ($\tilde{V}$) isotherms for different temperatures. The isotherms display oscillatory behaviour for temperatures below the critical temperature ($T_c$), which disappears for temperatures above $T_c$. (b) Reduced Gibbs free energy ($\tilde{G}$) versus reduced temperature ($\tilde{T}$) plots for various pressures ($P$). A swallowtail behaviour is observed for pressures below the critical pressure ($P_c$), characteristic of a van der Waals-like phase transition.
• Figure 2: Phase structure of the ABG AdS black hole. (a) In the $P$-$T$ plane, the solid orange curve represents the coexistence curve, while the dashed blue curves depict the spinodal curves. The region above the coexistence curve corresponds to the stable large black hole (LBH) phase, and below it to the stable small black hole (SBH) phase. The area between the spinodal curves indicates metastable phases. (b) In the $T$-$V$ plane, the area above the coexistence curve signifies unstable phases, and the area below denotes stable phases. The region between the coexistence and spinodal curves represents metastable phases. The critical temperature is marked by a red dot.
• Figure 3: Reduced horizon radius versus Hawking temperature. (a) An abrupt change at the critical temperature signifies a first-order phase transition. (b) The horizon radius behaves as an order parameter.
• Figure 4: Behaviour of effective potential of the black hole.
• Figure 5: (a) Temperature vs. photon sphere radius and (b) temperature vs. minimum impact parameter, for different values of pressure, show an oscillatory behaviour similar to vdW-like fluids.