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- Recently, several methods have been proposed to regularize a limit of Einstein–Gauss–Bonnet (EGB), leading to nontrivial gravitational dynamics in EGB gravity coupled to non-linear electrodynamics and analyze their thermodynamic properties to calculate precise expressions for the black hole mass, temperature, and entropy. Because of the magnetic charge, the thermodynamic quantities are corrected, and the Hawking–Page phase transition is achievable with diverges of the heat capacity at a larger critical radius in comparison to the counterpart where the temperature is maximum. Thus, we have a black hole with Cauchy and event horizons, and its evaporation leads to a thermodynamically stable extremal black hole remnant with vanishing temperature, and its size is larger than the counterpart. The entropy does not satisfy the usual exact horizon Bekenstein–Hawking area law of general relativity with a logarithmic area correction term.
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- We investigate the extended phase space thermodynamics of nonsingular-AdS black holes minimally coupled to clouds of strings in which we consider the cosmological constant () as the pressure (P) of the black holes and its conjugate variable thermodynamical volume (V) of the black holes. Owing to the background clouds of strings parameter (a), we analyse the Hawking temperature, entropy and specific heat on horizon radius for fixed-parameter k. We find that the strings clouds background does not alter small/large black hole (SBH/LBH) phase transition but occurs at a larger horizon radius, and two second-order phase transitions occur at a smaller horizon radius. Indeed, the G–T plots exhibit a swallowtail below the critical pressure, implying that the first-order phase transition is analogous to the liquid–gas phase transition at a lower temperature and lower critical pressure. To further examine the analogy between nonsingular-AdS black holes and a liquid–gas system, we derive the exact critical points and probe the effects of a cloud of strings on criticality to find that the isotherms undergo liquid–gas like phase transition for at lower . We have also calculated the critical exponents identical with Van der Walls fluid, i.e., same as those obtained before for arbitrary other AdS black holes, which implies that the background clouds of strings do not change the critical exponents.
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- We obtain exact Bardeen black holes to the regularized 4D Einstein–Gauss–Bonnet (EGB) gravity minimally coupled with the nonlinear electrodynamics (NED). In turn, we analyze the horizon structure to determine the effect of GB parameter on the minimum cutoff values of mass, M0, and magnetic monopole charge, g0, for the existence of a black hole horizon. We obtain an exact expression for thermodynamic quantities, namely, Hawking temperature T+, entropy S+, Helmholtz free energy F+, and specific heat C+ associated with the black hole horizon, and they show significant deviations from the 4D EGB case owing to NED. Interestingly, there exists a critical value of horizon radius, rc+, corresponding to the local maximum of Hawking temperature, at which heat capacity diverges, confirming the second-order phase transition. A discussion on the black holes of alternate regularized 4D EGB gravity belonging to the scalar-tensor theory is appended.
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