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Recently, a conjecture has been proposed, which indicates a correlation between super-entropy black holes and the thermodynamic instability \cite{Cong:2019bud}. W.Cong et al. suggested that the $C_{V}$ (specific heat capacity at constant volume) and $C_{P}$ (specific heat capacity at constant pressure) of a super-entropy black hole could not be greater than zero simultaneously as set in the extended phase space, which implies that the black hole is unstable in extended thermodynamics. This conjecture is intriguing and meaningful. Therefore, we did a study on that. After deriving the equations of specific heat capacities as well as plotting the relevant curves of the four-dimensional conformal black holes (a kind of super-entropy black hole), we obtained regions on the graphs where $C_{V}$ and $C_{P}$ are simultaneously greater than zero, which contradicts the conjecture that super-entropy black hole corresponds to its thermodynamic instability. Thus far, we have provided a counterexample to the hypothesis in \cite{Cong:2019bud}., 13 pages, 3 figures

In~\cite{Johnson:2019mdp}, Clifford put forward that the specific heat at constant volume $C_{V}$ is always negetive for the super-entropy black hole. Later in~\cite{Cong:2019bud}, Robert et al. found $C_{V}>0$ in certain region for the generalized exotic BTZ black holes. Futhermore, they proposed a new conjecture that as the $C_{V}>0$, the specific heat at constant pressure $C_{P}$ always satisfies $C_{P}0$ and meanwhile $C_{P}>0$. Hence, we find a counterexample to the two conjectures., 10 pages, 2 figures

In this paper, we characterize the phase transitons of Born-Infeld AdS black holes in terms of Lyapunov exponents. We calculate the Lyapunov exponents for both null and timelike geodesics. It is found that black hole phase transitions can be described by multiple-valued Lyapunov exponents. And its phase diagram can be characterized by Lyapunov exponents and Hawking temperature. Besides, the change of Lyapunov exponents can be considered as order parameter, and exists a critical exponent $1/2$ near critical point., Comment: 22 pages, 21 figures

In this paper, we investigate the effective potential and echoes from the dyonic black hole with quintessence. For a dyonic black hole, the quasi-topological electromagnetism provides proper matter energy-momentum tensor to curve the spacetime, and quintessence strengthens this force. We find that when the effect of quintessence becomes stronger, the black hole potential transforms between single-peak and double-peak, which will influence the existence of black hole echoes. In particular, we find that observer will receive a sudden vanishment of high-frequency echoes when quintessence remains a relatively strong effect., Comment: 15 pages, 8 figures

In this paper, we have studied the variation of the chaos bound in two regions of the torus-like black hole, i.e., the region close to the black hole horizon and the region at a certain distance from the black hole horizon. The angular momentum of the particle affects the effective potential and influences the magnitude of the chaotic behavior of the particle. Therefore, the angular momentum of particle is important in the study. The angular momentum of a particle not only affects the particle equilibrium orbital position, but also affects the Lyapunov exponent. As the angular momentum of the particle increases, the particle equilibrium position gradually moves away from the black hole horizon. In the near black hole horizon region, the chaos bound is not violated, however, at the far black hole horizon region, the chaos bound is violated. In addition unlike the charged AdS black hole which has a spherical topology of the horizon, the torus-like black hole has a toroidal topology of the horizon., 9 pages, 1 figures, 2 tables

In this paper, we extend Joule-Thomson expansion to the low-dimensional regime in rainbow gravity by considering the rainbow rotating BTZ metric in the (2+1)-dimensional spacetime. After the metric of the black hole is obtained, we get the Joule-Thomson expansion of the black hole, including the Joule-Thomson coefficient, inversion curves, and isenthalpic curves. We find that a rainbow rotating BTZ black hole does not have $P-V$ critical behavior. The effects of rainbow gravity are to slow down the trend of the increase of the Joule-Thomson coefficient and make its zero point larger. Moreover, the rainbow gravity slows down the inverse temperature of the black hole, meaning that a rainbow rotating BTZ black hole tends to change its heating or cooling action at a lower temperature, which can be attributed to the topology of the black hole., 14 pages, 7 figures, 2 tables

Doubly special relativity (DSR) is an effective model for encoding quantum gravity in flat spacetime. To incorporate DSR into general relativity, one could use gravity's rainbow, where the spacetime background felt by a test particle would depend on its energy. In this paper, we investigate the thermodynamics of rainbow Kerr black hole in the scenario with the stationary(ST) orthonormal frame and free-fall(FF) orthonormal frame. After the rainbow metric in ST frame and FF frame is deduced, the Hamilton-Jacobi method is used to acquire the modified Hawking temperature, specific heat and corresponding the modified entropy to each scenario, then the thermodynamic properties are discussed. We find that the effects of rainbow gravity on Kerr black holes are quite model-dependent. In other words, the value of parameter $\eta$ and $n$ with Amelino-Camelia's proposal are crucially important and worth discussing. Specificly, with most widly accepted choice ($n=2,\eta >0$), the effects of rainbow gravity tend to decrease the Hawking temperature but increase the black hole entropy in ST frame, and increase the Hawking temperature but decrease the black hole entropy in FF frame conversely., Comment: 15 pages, 8 figures, 2 tables. arXiv admin note: text overlap with arXiv:2205.02712

Herein, we focus on the study of Joule-Thomson expansion corresponding to a d-dimensional charged AdS black hole with cloud of strings and quintessence. Then its relevant solution and some thermodynamic properties are investigated. Specifically, we evaluate its Joule-Thomson expansion from four important aspects, including the Joule-Thomson coefficient, inversion curve, isenthalpic curve, and ratio $\frac{T_{i}^{min}}{T_{c}}$. After analysis, different dimensions with strings of cloud and quintessence parameters have different effects on the Joule-Thomson coefficient (the same situation are found for the inversion curve, isenthalpic curve, and ratio $\frac{T_{i}^{min}}{T_{c}}$)., Comment: 10 pages, 6 figures, 15 tables

In this paper, we investigated the chaos of the phantom AdS black hole in near-horizon regions and at a certain distance from the black hole, where the Lyapunov exponent was calculated by the Jacobian determinant. We found that the angular momenta of charged particles nearby the black hole affect the position of the equilibrium orbit as well as the Lyapunov exponent. When the charge is large enough and the angular momenta take particular values, the bound is violated at a certain distance from the event horizon. Concurrently, we compared the differences by analyzing tables and figures after taking different values of $\eta$, where $\eta$ is a constant indicating the nature of the electromagnetic field. When $\eta=1$, it corresponds to the Reissner-Nordstr$\ddot{o}$m-AdS black hole (RN-AdS black hole) and it represents the phantom AdS black hole when $\eta=-1$. In this way, we can draw the following conclusions. Under different values of $\eta$, the variation trends of curves related to $\lambda^{2}-\kappa^{2}$ could be different, where it can be judged whether the constraint is violated by determining if $\lambda^{2}-\kappa^{2}$ is greater than zero. In addition, the corresponding numerical values of angular momenta violating the bound in the phantom AdS black hole are much smaller than the case of RN-AdS black hole. But cases in these different black holes have the same rules to violate the bound. The large absolute values of charge and $\Lambda$ are more likely to violate the bound., Comment: 13 pages, 3 figures, 5 tables

In this paper, we investigate the thermodynamic properties of the RN-AdS black hole with cloud of strings and quintessence in rainbow gravity with the stationary (ST) orthonormal frame and the free-fall (FF) orthonormal frame. After the SF and the FF rainbow metric is obtained, we get the Hawking temperature and the entropy, and their physical meanings are discussed. We find that, for the ST rainbow RN-AdS black hole with cloud of strings and quintessence, the effect of rainbow gravity is to increase the Hawking temperature but decrease the entropy of the black hole. However, for the FF rainbow case, rainbow gravity turns out to decrease the Hawking temperature but increase the entropy of the black hole, which seems that the effects rainbow gravity has are quite model-dependent., Comment: 14 pages, 5 figures, 1 table

Recently, a new assumption was proposed in [Phys. Rev. D 100, no.10, 104022 (2019)]. This assumption considers that the energy of the particle changes the enthalpy of the black hole after throwing the particle into the black hole. Using the energy-momentum relation, the results show that the second law of thermodynamics of the black hole is valid in extended phase space. In this paper, we discuss the validity of the laws of thermodynamics and the stability of the horizon of the charged AdS black hole by scalar field scattering under two assumptions, i.e., the energy flux of the scalar field $dE$ changes the internal energy of the black hole $dU$ and the energy flux of the scalar field $dE$ changes the enthalpy of the black hole $dM$., 15 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:2103.08162

In this paper, the thermodynamics and the stability of horizon of the charged AdS black hole surrounded by quintessence and cloud of strings in d-dimensional spacetime are studied via the scalar field scattering and the charged particle absorption. The cosmological constant is interpreted as a thermodynamics variable. During the study, we consider the case where the energy of the particle(scalar field) is related to the internal energy of the black hole. Furthermore, we also consider another assumption, which is proposed in [Phys. Rev. D 100, no.10, 104022 (2019)]. This assumption considers that the energy of the particle(scalar field) is related to the internal energy of the black hole. In addition, we compare and discuss the results obtained under these two assumptions. At the same time, we also considered the effect of the dimension. The thermodynamics of black holes in different dimensions has also been studied and compared., Comment: 63 pages, 38 figures and 27 tables

By using the scattering of a scalar field, we discuss the thermodynamics and overcharging problem in a 4D Gauss-Bonnet AdS black hole in both the normal phase space and extended phase space. In the normal phase space, where the cosmological constant and Gauss-Bonnet parameter are fixed, the first law and the second law of thermodynamics are valid. In addiction, the black hole cannot be overcharged and the weak cosmic censorship conjecture is valid. In the extended phase space, where the cosmological constant and Gauss-Bonnet parameter are treated as the thermodynamic variables, the first law is still valid. However, the second law is indefinite. Moreover, after the scattering of the scalar field, the extremal black hole cannot be overcharged and the near-extremal black hole can be overcharged., 17 pages, 6 figures

The thermodynamics and overcharging problem in the RN-AdS black hole with the cloud of strings and quintessence are investigated by absorption of scalar particle and fermion in the extend phase space. The cosmological constant is treated as the pressure with a conjugate volume. Besides, the parameters related to quintessence and cloud of strings are treated as thermodynamic variables. Finally we find the first law of thermodynamics is satisfied and the second law of thermodynamics is indefinite. Furthermore, the near-extremal and extremal black holes can not be overcharged., 18 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:2008.08327

In this paper, we investigate effects of the minimal length on the Schwinger mechanism using the quantum field theory (QFT) incorporating the minimal length. We first study the Schwinger mechanism for scalar fields in both usual QFT and the deformed QFT. The same calculations are then performed in the case of Dirac particles. Finally, we discuss how our results imply for the corrections to the Unruh temperature and the Hawking temperature due to the minimal length., 14 pages