Impact of Thermodynamic Corrections on the Stability of Hayward-Anti de Sitter Black Hole Surrounded by a Fluid of Strings

TL;DR

This work studies the thermodynamics of a Hayward-AdS black hole immersed in a string-fluid environment, incorporating Hayward regularisation and quantum entropy corrections in an extended (pressure–volume) framework. By deriving corrected entropy $S_c$ and associated potentials $H_c$, $F_c$, and $G_c$, the authors analyze how the string-fluid parameters $(b,\varepsilon)$, regularisation scale $q$, and quantum-correction coefficients $(\lambda_1,\lambda_2)$ shape phase transitions. The results reveal a robust first-order SBH-LBH transition, evidenced by swallowtail structures in Gibbs free energy, with corrections smoothing the transition and stabilising the LBH phase; larger $q$, stronger string fluids, and quantum corrections generally promote LBH stability and shift $T_c$ to lower values. These findings illustrate the intertwined roles of classical gravity, exotic matter, and quantum effects in black-hole thermodynamics and offer potential implications for black-hole evolution, holography, and observational signatures.

Abstract

We explore the modified thermodynamics of a Hayward-Anti de Sitter (H-AdS) black hole in atypical conditions, incorporating a string fluid, Hayward regularisation, and quantum entropy corrections. Our analysis reveals a first-order phase transition between small and large black hole phases, characterised by a swallowtail behaviour in the Gibbs free energy profiles. It is found that the key parameters - string fluid strength, Hayward regularisation scale, and quantum correction coefficients significantly influence the critical temperature and phase stability of the H-AdS system. It is further noticed that a large black hole phase is stabilised by these modifications, with quantum corrections smoothing the transition. This model offers a valuable framework to study quantum gravity effects on black hole thermodynamics with potential implications in analysing black hole evolution and astrophysical observations.

Figures (8)

• Figure 1: Variation of the Hawking temperature $T_H$ with the black hole horizon radius $r_+$.
• Figure 2: Variation of the corrected black hole entropy ($S_c$) with the horizon radius ($r_+$)
• Figure 3: Variation of the corrected black hole enthalpy $H_c$ with the horizon radius $r_+$.
• Figure 4: Variation of corrected black hole Helmholtz free energy ($F_c$) with the horizon radius ($r_+$).
• Figure 5: Variation of the black hole $G_c$ with the horizon radius $r_+$.