View of thermodynamic phase transition of the charged Gauss-Bonnet AdS black hole via the shadow

We examine thermodynamic phase transition(PT)of the charged Gauss-Bonnet Ad S black hole(BH)by utilizing the shadow radius.In this system,we rescale the corresponding Gauss-Bonnet coefficientαby a factor of 1/(D-4),and ensure thatαis positive to avoid any singularity problems.The equation derived for the shadow radius indicates that it increases as the event horizon radius increases,making it an independent variable for determining BH temperature.By investigating the PT curve in relation to shadows,we can observe that the shadow radius can be used as an alternative to the event horizon radius in explaining the phenomenon of BH PT.Furthermore,the results indicate that an increase in the parameterαcorresponds to a decrease in the temperature of the BH.By utilizing the relationship between the temperature and the shadow radius,it is possible to obtain the thermal profile of the Gauss-Bonnet AdS BH.It is evident that there is an N-type variation in temperature for pressures P<P_(c).Additionally,as the parameterαincreases,the region covered by shadow expands while the temperature decreases.The utilization of BH shadows as a probe holds immense significance in gaining a deeper understanding of BH thermodynamic behavior.

Shadow thermodynamics of AdS black hole with the nonlinear electrodynamics term

We creatively employ the shadow radius to study the thermodynamics of a charged Ad S black hole with a nonlinear electrodynamics(NLED)term.First,the connection between the shadow radius and event horizon is constructed with the aid of the geodesic analysis.It turns out that the black hole shadow radius shows a positive correlation as a function of the event horizon radius.Then in the shadow context,we find that the black hole temperature and heat capacity can be presented by the shadow radius.Further analysis shows that the shadow radius can work similarly to the event horizon in revealing black hole phase transition process.In this sense,we construct the thermal profile of the charged Ad S black hole with inclusion of the NLED effect.In the P<Pc case,it is found that the N-type trend of the temperature given by the shadow radius is always consistent with that obtained by using the event horizon.Thus,we can conclude for the charged Ad S black hole that the phase transition process can be intuitively presented as the thermal profile in the shadow context.Finally,the effects of NLED are carefully analyzed.

Photon orbits and phase transition for Letelier AdS black holes immersed in perfect fluid dark matter

We obtain an exact solution for spherically symmetric Letelier AdS black holes immersed in perfect fluid dark matter(PFDM).Considering the cosmological constant as the positive pressure of the system and volume as its conjugate variable,we analyze the thermodynamics of our black holes in the extended phase space.Owing to the background clouds of strings parameter(a)and the parameter endowed with PFDM(β),we analyze the Hawking temperature,entropy,and specific heat.Furthermore,we investigate the relationship between the photon sphere radius and phase transition for the Letelier AdS black holes immersed in PFDM.Through the analysis,with a particular condition,non-monotonic behaviors are found between the photon sphere radius,impact parameter,PFDM parameter,temperature,and pressure.We can regard the changes in both the photon sphere radius and impact parameter before and after phase transition as the order parameter;their critical exponents near the critical point are equal to the same value,1/2,similar to that in ordinary thermal systems.This indicates that a universal relation of gravity may exist near the critical point for a black hole thermodynamic system.

Triple points and phase transitions of D-dimensional dyonic Ad S black holes with quasitopological electromagnetism in Einstein–Gauss–Bonnet gravity

By considering the negative cosmological constant Λ as a thermodynamic pressure, we study the thermodynamics and phase transitions of the D-dimensional dyonic Ad S black holes(BHs) with quasitopological electromagnetism in Einstein–Gauss–Bonnet(EGB) gravity. The results indicate that the small/large BH phase transition that is similar to the van der Waals(vdW) liquid/gas phase transition always exists for any spacetime dimensions. Interestingly, we then find that this BH system exhibits a more complex phase structure in 6-dimensional case that is missed in other dimensions.Specifically, it shows for D = 6 that we observed the small/intermediate/large BH phase transitions in a specific parameter region with the triple point naturally appeared. Moreover, when the magnetic charge turned off, we still observed the small/intermediate/large BH phase transitions and triple point only in 6-dimensional spacetime, which is consistent with the previous results. However, for the dyonic Ad S BHs with quasitopological electromagnetism in Einstein–Born–Infeld(EBI) gravity, the novel phase structure composed of two separate coexistence curves observed by Li et al. [Phys. Rev. D105 104048(2022)] disappeared in EGB gravity. This implies that this novel phase structure is closely related to gravity theories, and seems to have nothing to do with the effect of quasitopological electromagnetism. In addition, it is also true that the critical exponents calculated near the critical points possess identical values as mean field theory. Finally, we conclude that these findings shall provide some deep insights into the intriguing thermodynamic properties of the dyonic Ad S BHs with quasitopological electromagnetism in EGB gravity.

Restricted phase space thermodynamics of charged AdS black holes in conformal gravity

The thermodynamics of charged spherically symmetric AdS black holes in conformal gravity is revisited using the recently proposed restricted phase space(RPS) formalism.This formalism avoids all the bizarreness arising in the extended phase space formalism for this model.It is found that the charged AdS black holes in this model may belong to a new universality class that is different from all previously studied cases under the RPS formalism.Besides the distinguished isocharge T-S and isothermal Φ-Q_(e) behaviors,the absence of the Hawking-Page transition is another notable feature.However,in the high temperature limit,the thermodynamic behavior of the present model becomes exactly the same as that of the Einstein gravity and black hole scan models,which adds further evidence for the universality of the recently reported correspondence between high temperature AdS black holes and low temperature quantum phonon gases in nonmetallic crystals.

P-V criticality and Joule-Thomson expansion of charged AdS black holes in the Rastall gravity

We discuss the P-V criticality and the Joule-Thomson expansion of charged AdS black holes in the Rastall gravity. We find that although the equation-of-state of a charged AdS black hole in the Rastall gravity is related to the Rastall parameter λ, its reduced equation-of-state at the critical point is independent of the Rastall parameter λ, as is the case in the Einstein gravity where λ=0. This is the reason why the critical exponents are not related to the Rastall parameter λ. We also find that the inversion temperature Ti is related to the Rastall parameter λ,but that the minimum inversion temperature Timin and the ratio ε between the minimum inversion temperature and the critical temperature are both independent of the Rastall parameter λ. At the critical point, the thermodynamic evolution of a charged AdS black hole in the Rastall gravity behaves as in the van der Waals fluid and charged AdS black hole in the Einstein gravity. We show the inversion curves and isenthalpic curves in the T-P plane and analyze the effect of the Rastall constant λ on the inversion curves of a charged AdS black hole during the Joule-Thomson expansion.

Joule–Thomson expansion of higher dimensional nonlinearly AdS black hole with power Maxwell invariant source

In this paper,the Joule–Thomson expansion of the higher dimensional nonlinearly anti-de Sitter(Ad S)black hole with power Maxwell invariant source is investigated.The results show the Joule–Thomson coefficient has a zero point and a divergent point,which coincide with the inversion temperature Tiand the zero point of the Hawking temperature,respectively.The inversion temperature increases monotonously with inversion pressure.For the high-pressure region,the inversion temperature decreases with the dimensionality D and the nonlinearity parameter s,whereas it increases with the charge Q.However,Tifor the low-pressure region increase with D and s,while it decreases with Q.The ratioηBHbetween the minimum inversion temperature and the critical temperature does not depend on Q,it recovers the higher dimensional Reissner–N?rdstrom Ad S black hole case when s=1.However,for s>1,it becomes smaller and smaller as D increases and approaches a constant when D→∞.Finally,we found that an increase of mass M and s,or reducing the charge Q and D can enhance the isenthalpic curve,and the effect of s on the isenthalpic curve is much greater than other parameters.

Photon sphere and phase transition of ddimensional(d≥5) charged Gauss–Bonnet AdS black holes

Motivated by recent work,nonmonotonic behaviors of photon sphere radius can be used to reflect black hole phase transition for Reissner–Nordstr?m–AdS(RN–AdS)black holes,we study the case of five-dimensional charged Gauss–Bonnet–AdS black holes in the reduced parameter space.We find that the nonmonotonic behaviors of photon sphere radius still exist.Using the coexistence line calculated from P–V plane,we capture the photon sphere radius of saturated small and large black holes(the boundary of the coexistence phase),then illustrate the reduced coexistence region.The results show that,reduced coexistence region decreases with charge Q but increases with Gauss–Bonnet coefficientα.When the charge vanishes,reduced coexistence region does not vary with Gauss–Bonnet coefficientαany more.In this case,the Gauss–Bonnet coefficientαplays the same role as the charge of five-dimensional RN–AdS black holes.Also,the situation of higher dimension is studied in the end.

A new measure of thermal micro-behavior for the AdS black hole

In spired by the hypothesis of the black hole molecule,with the help of the Hawking temperature,entropy,and the thermodynamic curvature of black holes,we propose a new measure of the relation between the interaction and the thermal motion of molecules of the AdS black hole as a preliminary and coarse-grained description.The proposed measure introduces a dimensi on less ratio to characterize this relation and shows that there is indeed competition between the in teractions of black hole molecules and their thermal motion.For a charged AdS black hole,below the critical dimensionless pressure,there are three transitions between the interaction and thermal motion states.In contrast,above the critical dimensionless pressure,only one transition takes place.For the Schwarzschild-AdS and five-dimensional Gauss-Bonnet AdS black holes,a transition always occurs between the interaction and thermal motion states.

Joule-Thomson expansion of Born-Infeld AdS black holes

In this paper,the Joule-Thomson expansion of Born-Infeld AdS black holes is studied in the extended phase space,where the cosmological constant is identified with the pressure.The Joule-Thomson coefficient,the inversion curves and the isenthalpic curves are discussed in detail using a 4-dimensional black hole.The critical point of a Born-Infeld black hole is depicted with varying parameter β and the charge Q.In T-P plane,the inversion temperature curves and isenthalpic curves are obtained with different parameter β and charge Q.We find that the missing negative slope is still conserved in Born-Infeld black holes.We also extend our discussion to arbitrary dimension higher than 4.The critical temperature and the minimum of inversion temperature are compared.The ratio is asymptotically 1/2 as Q increases or β→∞ with D=4 ,and reproduces previous results at higher dimensions.

Instability of AdS black holes with lattices

Anti-de Sitter(AdS)black holes with lattices are essential for optical conductivity studies in the holographic approach.We investigate the instability of these black holes that can result in the holographic description of charge density waves.In the presence of homogeneous axion fields,we show that the instability of AdS-Reissner-Nordström(AdS-RN)black holes is always suppressed.However,in the presence of Q-lattices,we find that the unstable region becomes the smallest in the vicinity of the critical region for the metal/insulator phase transition.This novel phenomenon is reminiscent of the behavior of the holographic entanglement entropy during quantum phase transitions.

Gravitational quasi-normal modes of static R^2 Anti-de Sitter black holes

In this paper, we study the gravitational quasi-normal modes（QNMs） for a static R^2 black hole（BH） in Anti-de Sitter（AdS） spacetime. The corresponding master equation of odd parity is derived and the QNMs are evaluated by the Horowitz and Hubeny method. Meanwhile the stability of such BH is also discussed through the temporal evolution of the perturbation field. Here we mainly consider the coefficient λ, which is related to the radius of AdS black hole, on the QNMs of the R^2 AdS BH. The results show that the Re（ω） and ｜Im（ω）｜ of the QNMs increase together as ｜λ｜ increases for a given angular momentum number l. That indicates with a larger value of ｜λ｜ the corresponding R^2 AdS BH returns to stable much more quickly. The dynamic evolution of the perturbation field is consistent with the results derived by the Horowitz and Hubeny method. Since in the conformal field theory the QNMs can reflect its approach to equilibrium, so our related results could be referential to studies of the AdS/CFT conjecture. The relationship between λ and the properties of the static R^2 BH might be helpful for the development of R^2 gravitational theory.

Joule-Thomson Expansion of d-Dimensional Charged Anti-de Sitter Black Holes Surrounded by Quintessence with a Cloud of Strings Background

Effects of the dimension on the Joule-Thomson expansion are investigated in details by considering the case of d-dimensional(d≥5)charged anti-de Sitter(AdS)black hole which is surrounded by the quintessence with a cloud of strings background.Firstly,the thermodynamic quantity of this black hole is reviewed.Secondly,three important features of the Joule-Thomson expansion in different dimensions are discussed,including the Joule-Thomson coefficients,inversion curves,and isenthalpic curves.Finally,the effects of the charge,the quintessence and strings cloud parameters on the Joule-Thomson expansion in the case of six-dimensional black hole are studied.

Phase transition of non-linear charged Anti-de Sitter black holes

Understanding the thermodynamic phase transition of black holes can provide a deep insight into the fundamental properties of black hole gravity to establish the theory of quantum gravity.We investigate the condition and latent heat of phase transition for non-linear charged AdS black holes using Maxwell's equal-area law.In addition,we analyze the boundary and curve of the two-phase coexistence area in the expanded phase space.We suggest that the phase transition of the non-linear charged AdS black hole with the fixed temperature(T<T_(c))is related to the electric potential at the horizon,not only to the location of black hole horizon.Recently,the molecular number density was introduced to study the phase transition and microstructure of black holes.On this basis,we discuss the continuous phase transition of a non-linear charged AdS black hole to reveal the potential microstructure of a black hole by introducing the order parameter and using the scalar curvature.

Dynamic property of phase transition for non-linear charged anti-de Sitter black holes

Understanding the thermodynamic phase transition of black holes can provide deep insights into the fundamental properties of black hole gravity and help to establish quantum gravity.In this work,we investigate the phase transition and its dynamics for the charged EPYM AdS black hole.Through reconstructing Maxwell's equal-area law,we find there exists a high-/low-potential black hole(HPBH/LPBL)phase transition,not only the pure large/small black hole phase transition.The Gibbs free energy landscape(G_(L))is treated as a function of the black hole horizon,which is the order parameter of the phase transition due to thermal fluctuation.From the viewpoint of G_(L),the stable HPBH/LPBL states correspond to two wells of G_(L),which have the same depth.The unstable intermediate-potential black hole state corresponds to the local maximum of G_(L).Then we focus on the probability evolution governed by the Fokker-Planck equation.Through solving the Fokker-Planck equation with different reflection/absorption boundary conditions and initial conditions,the dynamics of switching between the coexistent HPBH and LPBL phases is probed within the first passage time.Furthermore,the effect of temperature on the dynamic properties of the phase transition is also investigated.

Shadow thermodynamics of non-linear charged Anti-de Sitter black holes

It is well known that when vacuum polarization emerges in quantum electrodynamics,the non-linear interaction between electromagnetic fields should be considered.Moreover,the corresponding field of non-linear electrodynamics can have important effects on black hole physics.In this work,we focus on the relationship between an observable quantity,that is,the shadow radius,and the first-order phase transition of non-linear charged AdS black holes in the framework of Einstein-power-Yang-Mills gravity.The results show that,under a certain condition,there exists a first-order phase transition from the viewpoint of both the shadow radius and horizon radius,which depend on temperature(or pressure).From the viewpoint of the shadow radius,the phase transition temperature is higher than that from the viewpoint of the horizon radius under the same condition.This may be due to the non-linear Yang Mills charge and the gravitational effect.This indicates that the shadow radius can be regarded as a probe to reveal the thermodynamic phase transition information of black holes.The thermal profiles of coexistent large and small black hole phases when the system is undergoing the phase transition are presented for two different values of the non-linear Yang Mills charge parameter:γ=1,1.5.Furthermore,the effects of the non-linear Yang Mills charge parameter on the shadow radius and thermal profile are investigated.

Dynamic phase transition of charged dilaton black holes

The dynamic phase transition of charged dilaton black holes is investigated in this paper.The Gibbs free energy landscape is introduced,and the corresponding G_(L) is calculated for the dilaton black hole.We numerically solve the Fokker-Planck equation constrained by only the reflecting boundary condition.The effects of dilaton gravity on the probabilistic evolution of dilaton black holes are explored.Firstly,the horizon radius difference between a large dilaton black hole and a small dilaton black hole increases with the parameterα.Secondly,with increasingα,the system needs much more time to achieve a stationary distribution.Finally,the values attained forρ(rl,t)andρ(rs,t)vary withα.Additionally,by resolving the Fokker-Planck equation constrained by both the reflecting boundary condition and absorbing boundary condition,we investigate the first passage process of dilaton black holes.The initial peak decays more slowly with increasingα,which can also be observed via the slowing decay ofΣ(t)(the sum of the probability of the black hole system not having completed a first passage by time t).Moreover,the time corresponding to the single peak of the first passage time distribution is found to increase with the parameterα.Considering these observations,the dilaton field is found to slow down the dynamic phase transition process between a large black hole and a small black hole.