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.

Thermodynamic Curvature and Phase Transitions from Black Hole with a Coulomb-Like Field

In this paper, we first investigate the thermodynamic features of the black hole with a coulomb-like field. Moreover, we obtain the geometric description of the black hole thermodynamics. We find that for the black hole with a coulomb-like field the Weinhold geometry is fiat, whereas its Ruppeiner geometry is curved. For the heat capacity and curvature calculation shows the Ruppeiner geometry has a transition point.

Thermodynamic geometry of the Garfinkle-Horowitz-Strominger dilaton black hole

This paper studies the thermodynamic properties of the Garfinkle Horowitz Strominger dilaton black hole from the viewpoint of geometry. It calculates the heat capacity and the temperature of the black hole, Weinhold metric and Ruppeiner metric are also obtained respectively. It finds that they are both curved and the scalar curvature of the Weinhold geometry consists with the first-order transition point reproduced from the capacity, while the Ruppeiner one is both in accordance with the first-order and the second-order phase transition points reproduced from the capacity.

Temperature and thermodynamic geometry of the Kerr-Sen black hole

This paper studies the thermodynamic properties of the Kerr-Sen black hole from the viewpoint of geometry. It calculates the temperature and heat capacity of the black hole, Weinhold metric and Ruppeiner metric are also obtained respectively. It finds that they are both curved and the curvature scalar of Weinhold curvature implies no information about the phase transition while the Ruppeiner one does. But they both carry no information about the second-order phase transition point reproduced from the capacity. Besides, the Legendre invariant metric of the Kerr-Sen black hole has been discussed and its scalar curvature gives the information about the second-order phase transition point.

Phase Transition and Quasinormal Modes for Spherical Black Holes in 5D Gauss–Bonnet Gravity

We study the quasinormal modes（QNMs） of massless scalar perturbations to probe the van der Waals like SBH/LBH phase transition of anti-de Sitter black holes in five-dimensional（5D） Gauss–Bonnet gravity. It is found that the signature of this SBH/LBH phase transition is detected when the slopes of the QNMs frequency change drastically and differently in small and large black holes near the critical point. The obtained results further support that the QNMs can be a dynamic probe to investigate the thermodynamic properties in black holes.

Geometry and thermodynamics of smeared Reissner–Nordstrm black holes in d-dimensional AdS spacetime

We construct a family of d-dimensional Reissner–Nordstrom-AdS black holes inspired by noncommutative geometry. The density distribution of the gravitational source is determined by the dimension of space, the minimum length of spacetime l, and other parameters（e.g., n relating to the central matter density）. The curvature of the center and some thermodynamic properties of these black holes are investigated. We find that the center of the source is nonsingular for n 0（under certain conditions it is also nonsingular for-2 n 〈 0）, and the properties at the event horizon, including the Hawking temperature, entropy, and heat capacity, are regular for n 〉-2. Due to the presence of l, there is an exponentially small correction to the usual entropy.

Notes on Phase Transition of Nonsingular Black Hole

On the belief that a black hole is a thermodynamic system, we study the phase transition of nonsingular black holes. If the black hole entropy takes the form of the Bekenstein-Hawking area law, the black hole mass M is no longer the internal energy of the black hole thermodynamic system. Using the thermodynamic quantities, we calculate the heat capacity, thermodynamic curvature and free energy. It is shown that there will be a larger black hole/smaller black hole phase transition for the nonsingular black hole. At the critical point, the second-order phase transition appears.

Thermodynamic and geometric framework of a(2+1)-dimensional black hole with non-linear electrodynamics

The thermodynamic properties of a （2 ＋ 1）-dimensional black hole with non-linear electrodynamics from the viewpoint of geometry is studied and some kinds of temperatures of the black hole have been obtained. Weinhold curvature and Ruppeiner curvature are explored as information geometry. Moreover, based on Quevedo＇s theory, the Legendre invariant geometry is investigated for the black hole. We also study the relationship between the scalar curvatures of the above several metrics and the phase transitions produced from the heat capacity.

Thermodynamics and weak cosmic censorship conjecture of charged AdS black hole in the Rastall gravity with pressure

Treating the cosmological constant as a dynamical variable,we investigate the thermodynamics and weak cosmic censorship conjecture(WCCC)of a charged AdS black hole(BH)in the Rastall gravity.We determine the energy momentum relation of charged fermion at the horizon of the BH using the Dirac equation.Based on this relation,it is shown that the first law of thermodynamics still holds as a fermion is absorbed by the BH.However,the entropy of both the extremal and near-extremal BH decreases in the irreversible process,which means that the second law of thermodynamics is violated.Furthermore,we verify the validity of the WCCC by the minimum values of the metric function h(r)at its final state.For the extremal charged AdS BH in the Rastall gravity,we find that the WCCC is always valid since the BH is extreme.While for the case of near-extremal BH,we find that the WCCC could be violable in the extended phase space(EPS),depending on the value of the parameters of the BH and their variations.

Thermodynamic phase transition and winding number for the third-order Lovelock black hole

Phase transition is important for understanding the nature and evolution of the black hole thermodynamic system.In this study,we predicted the phase transition of the third-order Lovelock black hole using the winding numbers in complex analysis,and qualitatively validated this prediction by the generalized free energy.For the 7<d<12-dimensional black holes in hyperbolic topology and the 7-dimensional black hole in spherical topology,the winding number obtained is three,which indicates that the system undergoes first-order and second-order phase transitions.For the 7<d<12-dimensional black holes in spherical topology,the winding number is four,and two scenarios of phase transitions exist,one involving a purely second-order phase transition and the other involving simultaneous first-order and second-order phase transitions.This result further deepens the research on black hole phase transitions using the complex analysis.

P-V Criticality of a Modified BTZ Black Hole in 2 + 1 Dimensional Intrinsic Time Quantum Gravity

Intrinsic time quantum geometrodynamics is a formulation of quantum gravity naturally adapted to 3 + 1 dimensions. In this paper we construct its analogous 2 + 1 formulation, taking note of the mathematical structures which are preserved. We apply the resulting construction to convert the BTZ black hole metric to ITQG framework. We then modify the BTZ black hole in order to investigate the existence of the P-V criticality in ITQG theory.

Thermodynamic geometry of the RN-Ad S black hole and non-local observables

This paper studies the thermodynamic geometry of the Reissner–Nordstr?m-anti-de Sitter(RN-AdS)black hole via detection of the non-local observables in the dual field theory,including the entanglement entropy and equal-time two-point correlation function.With the dimensional analysis,we construct the principle of corresponding states of black hole thermodynamics.As a result,our findings can be applied to black holes with different Ad S backgrounds.In this sense,the probe of the thermodynamic geometry of the RN-Ad S black hole though the non-local observables in dual field theory has been confirmed numerically.

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.

The thermodynamic stability and phase structure of the Einstein-Euler-Heisenberg-AdS black holes

In both the canonical ensemble and grand canonical ensemble,the thermodynamic stability and phase structure of Einstein-Euler-Heisenberg-AdS black holes are studied.We derive the Hawking temperature,Helmholtz free energy,Gibbs potential,entropy and heat capacity of the black holes.We compute the minimum temperature to find that a phase transition may happen at the lowest point.The entropy-temperature diagram consists of two parts.The upper part belonging to the large black holes under the influence from the electromagnetic self-interactions keeps the positive heat capacity,leading the huge compact objects to survive.The lower curves corresponding to small black holes show that the heat capacity of the tiny black holes is negative,which means that the nonlineareffect-corrected smaller sources will evaporate.The further discussions show that the nonlinear effect modifies the thermodynamic quantities,but the corrections limited by the nonlinear factorμwith allowed values can not change the properties and the phase structure fundamentally and thoroughly.We argue that the influence from self-interaction can not make the Einstein-Euler-Heisenberg-AdS black holes to split under the second law of thermodynamics.

Observing dynamic oscillatory behavior of triple points among black hole thermodynamic phase transitions

Understanding the dynamic process of black hole thermodynamic phase transitions at a triple point is a huge challenge. In this paper, we conduct the first investigation of dynamic phase behavior at a black hole triple point. By numerically solving the Smoluchowski equation near the triple point for a six-dimensional charged Gauss-Bonnet anti-de Sitter black hole, we report that initial small, intermediate, or large black holes can transit to the other two coexistent phases at the triple point, indicating that thermodynamic phase transitions can indeed occur dynamically. More significantly, we observe characteristic weak and strong oscillatory behavior in this dynamic process, which can be understood from an investigation of the rate of first passage from one phase to another. Our results further an understanding of the dynamic process of black hole thermodynamic phase transitions.

QED effects on phase transition and Ruppeiner geometry of Euler-Heisenberg-AdS black holes

Considering the quantum electrodynamics(QED)effect,we study the phase transition and Ruppeiner geometry of Euler-Heisenberg anti-de Sitter black holes in the extended phase space.For negative and small positive QED parameters,we observe a small/large black hole phase transition and reentrant phase transition,respectively,whereas a large positive value of the QED parameter ruins the phase transition.Phase diagrams for each case are explicitly shown.Then,we construct the Ruppeiner geometry in thermodynamic parameter space.Different features of the corresponding scalar curvature are shown for both the small/large black hole phase transition and reentrant phase transition cases.Of particular interest is the additional region of positive scalar curvature,indicating a dominant repulsive interaction among black hole microstructures,for the black hole with a small positive QED parameter.Furthermore,universal critical phenomena are observed for the scalar curvature of Ruppeiner geometry.These results indicate that the QED parameter has a crucial influence on the black hole phase transition and microstructure.

Thermodynamics and phase transition of topological dS black holes with a nonlinear source

We discuss black hole solutions of Einstein-Λ gravity in the presence of nonlinear electrodynamics in dS spacetime.Considering the correlation of the thermodynamic quantities respectively corresponding to the black hole horizon and cosmological horizon of dS spacetime and taking the region between the two horizons as a thermodynamic system,we derive effective thermodynamic quantities of the system according to the first law of thermodynamics,and investigate the thermodynamic properties of the system under the influence of nonlinearity parameter α.It is shown that nonlinearity parameter α influences the position of the black hole horizon and the critical state of the system,and along with electric charge has an effect on the phase structure of the system,which is obvious,especially as the effective temperature is below the critical temperature.The critical phase transition is proved to be second-order equilibrium phase transition by using the Gibbs free energy criterion and Ehrenfest equations.

Null geodesics,quasinormal modes,and thermodynamic phase transition for charged black holes in asymptotically flat and dS spacetimes

A numerical study has indicated that there exists a relation between the quasinormal modes and the Davies point for a black hole.In this paper,we analytically study this relation for charged Reissner-Nordstrom black holes in asymptotically flat and de Sitter(dS)spacetimes in the eikonal limit,under which the quasinormal modes can be obtained from the null geodesics using the angular velocity Ω and the Lyapunov exponentλof the photon sphere.Both in asymptotically flat and dS spacetimes,we observe spiral-like shapes in the complex quasinormal mode plane.However,the starting point of the shapes does not coincide with the Davies point.Nevertheless,we find a new relation in which the Davies point exactly meets the maximum temperature T in the T-Ω and T-λ planes.In a higher-dimensional asymptotically flat spacetime,although there is no spiral-like shape,such a relation still holds.Therefore,we provide a new relation between black hole thermodynamics and dynamics in the eikonal limit.Applying this relation,we can test the thermodynamic property of a black hole using the quasinormal modes.

Thermodynamics of charged black holes in Maxwell-dilaton-massive gravity

Considering the nonminimal coupling of the dilaton field to the massive graviton field in Maxwelldilaton-massive gravity,we obtain a class of analytical solutions of charged black holes,which are neither asymptotically flat nor(A)dS.The calculated thermodynamic quantities,such as mass,temperature,and entropy,verify the validity of the first law of black hole thermodynamics.Moreover,we further investigate the critical behaviors of these black holes in the grand canonical and canonical ensembles and find a novel critical phenomenon never before observed,known as the"reverse"reentrant phase transition with a tricritical point.It implies that the system undergoes a novel"SBH-LBH-SBH"phase transition process and is the reverse of the"LBH-SBH-LBH"process observed in reentrant phase transitions.

Hawking-Page transition and the dual relations of anti-de Sitter black holes surrounded by dark energy in general dimensions

Recently,a dual relation T_(0)(n+1)=T_(HP)(n)between the minimum temperature(T_(0)(n+1))black hole phase and the Hawking-Page transition(T_(HP)(n))black hole phase in two successive dimensions was introduced by Wei et al(2020 Phys.Rev.D10210411);this was reminiscent of the anti-de Sitter/conformal field theory(AdS/CFT)correspondence,as the Hawking-Page transition temperature could be treated as the temperature of the dual physical quantity on the boundary and the latter corresponds to that in the bulk.In this paper,we discuss the Hawking-Page transition and the dual relations in Ads black holes surrounded by dark energy in general dimensions.Our findings reveal the occurrence of the Hawking-Page transition between the thermal AdS radiation and thermodynamically stable large AdS black holes,in both the spacetime surrounded by phantom dark energy and the spacetime surrounded by quintessence dark energy.We discuss the effects of the phantom dark energy and quintessence dark energy on the Hawking-Page transition temperature.For the dual relation in particular,it works well for the case of an AdS black holes surrounded by phantom dark energy.For the case of an Ads black hole surrounded by quintessence dark energy,the dual relation should be modified under an open assumption that the state parameter and the density parameter of the quintessence dark energy depend on the dimensions of the spacetime.