Thermodynamics and weak cosmic censorship conjecture of an AdS black hole with a monopole in the extended phase space

The first law of black hole thermodynamics has been shown to be valid in the extended phase space.However,the second law and the weak cosmic censorship conjecture have not been investigated extensively.We investigate the laws of thermodynamics and the weak cosmic censorship conjecture of an AdS black hole with a global monopole in the extended phase space in the case of charged particle absorption.It is shown that the first law of thermodynamics is valid,while the second law is violated for the extremal and near-extremal black holes.Moreover,we find that the weak cosmic censorship conjecture is valid only for the extremal black hole,and that it can be violated for the near-extremal black holes,which is different from the previous results.     

Thermodynamics and weak cosmic censorship conjecture of 4D Gauss-Bonnet-Maxwell black holes via charged particle absorption

Recently, the non-trivial solutions for 4-dimensional black holes of Einstein-Gauss-Bonnet gravity had been discovered. In this paper, considering a charged particle entering into a 4-dimensional Gauss-Bonnet-Maxwell black hole, we calculate the black hole thermodynamic properties using the Hamilton-Jacobi equation. In the normal phase space, the cosmological constant and Gauss-Bonnet parameter are fixed, the black hole satisfies the first and second laws of thermodynamics, and the weak cosmic censorship conjecture (WCCC) is valid. On the other hand, in the case of extended phase space, the cosmological constant and Gauss-Bonnet parameter are treated as thermodynamic variables. The black hole also satisfies the first law of thermodynamics. However, the increase or decrease in the black hole's entropy depends on some specific conditions. Finally, we observe that the WCCC is violated for the near-extremal black holes in the extended phase space.     

Validity of thermodynamic laws and weak cosmic censorship for AdS black holes and black holes in a cavity

By throwing a test charged particle into a Reissner-Nordstrom (RN) black hole, we test the validity of the first and second laws of thermodynamics and the weak cosmic censorship conjecture (WCCC) with two types of boundary conditions: the asymptotically anti-de Sitter (AdS) space and a Dirichlet cavity wall placed in an asymptotically flat space. For the RN-AdS black hole, the second law of thermodynamics is satisfied, and the WCCC is violated for both extremal and near-extremal black holes. For the RN black hole in a cavity, the entropy can either increase or decrease depending on the change in the charge, and the WCCC is satisfied/violated for the extremal/near-extremal black hole. Our results indicate that there may be a connection between the black hole thermodynamics and the boundary condition imposed on the black hole.     

Weak cosmic censorship conjecture and thermodynamics in quintessence AdS black hole under charged particle absorption

Considering the cosmological constant as the pressure, this study addresses the laws of thermodynamics and weak cosmic censorship conjecture in the Reissner-Nordstr?m-AdS black hole surrounded by quintessence dark energy under charged particle absorption. The first law of thermodynamics is found to be valid as a particle is absorbed by the black hole. The second law, however, is violated for the extremal and near-extremal black holes, because the entropy of these black hole decrease. Moreover, we find that the extremal black hole does not change its configuration in the extended phase space, implying that the weak cosmic censorship conjecture is valid. Remarkably, the near-extremal black hole can be overcharged beyond the extremal condition under charged particle absorption. Hence, the cosmic censorship conjecture could be violated for the near-extremal black hole in the extended phase space. For comparison, we also discuss the first law, second law, and the weak cosmic censorship conjecture in normal phase space, and find that all of them are valid in this case.     

Weak cosmic censorship conjecture in the nonlinear electrodynamics black hole under the charged scalar field

In this paper, we study the thermodynamics and the weak cosmic censorship conjecture of the nonlinear electrodynamics black hole under the scattering of a charged complex scalar field.According to the energy and charge fluxes of the scalar field, the variations of this black hole's energy and charge can be calculated during an infinitesimal time interval. With scalar field scattering, the variation of the black hole is calculated in the extended and normal phase spaces.In the normal phase space, the cosmological constant and the normalization parameter are fixed,and the first and second laws of thermodynamics can also be satisfied. In the extended phase space, the cosmological constant and the normalization parameter are considered as thermodynamic variables, and the first law of thermodynamics is valid, but the second law of thermodynamics is not valid. Furthermore, the weak cosmic censorship conjecture is both valid in the extended and normal phase spaces.     

Entropy of three-dimensional BTZ black holes

~~Entropy of three-dimensional BTZ black holes~~     

Fermionic wigs for BTZ black holes

We compute the wig for the BTZ black hole, namely the complete non-linear solution of supergravity equations with all fermionic zero modes. We use a “gauge completion” method starting from _AdS3${\mathit{AdS}}_3$ Killing spinors to generate the gravitinos fields associated to the BH and we compute the back-reaction on the metric. Due to the anticommutative properties of the fermionic hairs the resummation of these effects truncates at some order. We illustrate the technique proposed in a precedent paper in a very explicit and analytical form. We also compute the mass, the angular momentum and other charges with their corrections.     

Weak cosmic censorship conjecture in BTZ black holes with scalar fields

The weak cosmic censorship conjecture in the near-extremal BTZ black hole has been tested using test particles and fields.It has been claimed that such a black hole can be overspun.In this paper,we review the thermodynamics and weak cosmic censorship conjecture in BTZ black holes using the scattering of a scalar field.The first law of thermodynamics in the non-extremal BTZ black hole is recovered.For the extremal and near-extremal black holes,due to the divergence of the variation of entropy,we test the weak cosmic censorship conjecture by evaluating the minimum of the function f,and find that both the extremal and near-extremal black holes cannot be overspun.     

Weak gravity conjecture from conformal field theory: a challenge from hyperscaling violating and Kerr-Newman-AdS black holes

We search for a possible relationship between weak gravity conjecture (WGC) and conformal field theory (CFT) in hyperscaling violating and Kerr-Newman-AdS black holes. We deal with the critical points of the black hole systems using the correlation function introduced in CFT and discuss WGC conditions using the imaginary part of the energy obtained from the critical points and their poles. Under the assumptions \begin{document}$ z=1 $\end{document}, \begin{document}$ d=1 $\end{document}, and \begin{document}$ \theta\rightarrow0^{-} $\end{document}, we link WGC to hyperscaling violating black holes owing to the existence of \begin{document}$ r_{H} $\end{document} values larger and smaller than one. For the second black hole system, we study the conditions of WGC for Kerr-Newman-AdS black holes using rotation and radius parameters. Then, we show that the conditions of WGC are satisfied when the charged particle near the hyperscaling violating and Kerr-Newman black holes is \begin{document}$ \frac{1}{a} $\end{document} with a ratio \begin{document}$ \frac{a}{\ell}\ll 1 $\end{document}.     

Thermodynamics of black holes in the quintessential phase space

Considering that the negative pressure of the accelerated expansion of the universe results from the cosmological constant or the dark energy quintessence, we use the dark energy quintessence to construct the "quintessential" phase space. In contrast to the previous discussion in which the cosmological constant is considered as the black hole (BH) phase transition pressure, in this analysis, we believe that the pressure results from quintessence. The characteristics of critical behavior, Gibbs free energy, and temperature behavior in quintessential phase space are investigated. We observe that the phase transition belongs to van der Waals phase transition within\begin{document}$ -1 <\omega_{\rm q}<-2/3 $\end{document}. If \begin{document}$ \omega_{\rm q} $\end{document}is within (–2/3, –1/3), the phase transition loses the large BH phase transition characteristics, which is caused by the later stage of the phase transition being completely dominated by quintessence dark energy with negative pressure. These results suggest that the quintessential phase space can be constructed with the pressure from the thermal quintessence, and it can be used as a new probe to explore the thermodynamics of BHs.     

Revisiting black hole thermodynamics in massive gravity: charged particle absorption and infalling shell of dust

In this study, we apply two methods to consider the variation of massive black holes in both normal and extended thermodynamic phase spaces. The first method considers a charged particle being absorbed by the black hole, whereas the second considers a shell of dust falling into it. With the former method, the first and second laws of thermodynamics are always satisfied in the normal phase space; however, in the extended phase space, the first law is satisfied but the validity of the second law?of?thermodynamics depends upon the model parameters. With the latter method, both laws are valid. We argue that the former method's violation of the second law of thermodynamics may be attributable to the assumption that the change of internal energy of the black hole is equal to the energy of the particle. Finally, we demonstrate that the event horizon always ensures the validity of weak cosmic censorship in both phase spaces; this means that the violation of the second law of thermodynamics, arising under the aforementioned assumption, does not affect the weak cosmic censorship conjecture. This further supports our argument that the assumption in the first method is responsible for the violation and requires deeper treatment.     

Thermodynamics of noncommutative geometry inspired black holes based on Maxwell-Boltzmann smeared mass distribution

In order to further explore the effects of non-Gaussian smeared mass distribution on the thermodynamical properties of noncommutative black holes, we consider noncommutative black holes based on Maxwell-Boltzmann smeared mass distribution in (2+1)-dimensional spacetime. The thermodynamical properties of the black holes are investigated, including Hawking temperature, heat capacity, entropy and free energy. We find that multiple black holes with the same temperature do not exist, while there exists a possible decay of the noncommutative black hole based on Maxwell-Boltzmann smeared mass distribution into the rotating (commutative) BTZ black hole.     

Thermodynamics in rotating anti-de Sitter black holes with massive scalar field in three dimensions

We investigated the tendency in the variations of CFT₂ when a rotating AdS₃ black hole changes because of the fluxes transferred by the scattering of a massive scalar field according to the anti-de Sitter (AdS)/conformal field theory (CFT) correspondence. The conserved quantities of the black hole are definitely constrained by the extremal condition. Moreover, the laws of thermodynamics provide a direction for the changes in the conserved quantities. Therefore, the black hole cannot be extremal under the scattering; this is naturally preferred. According to the relationship between the rotating AdS₃ black hole and dual CFT₂, we find that such changes in the black hole constrain the variations in the eigenstates of dual CFT₂. Furthermore, the tendency in the variations is closely related to the laws of thermodynamics.     

Quasistationary collapse to the extreme Kerr black hole

It is shown that the extreme Kerr black hole, i.e. the one with the maximal angular momentum for a given mass, is the only candidate for a black hole limit of rotating fluid bodies in equilibrium.     

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 Ad S 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 Ad S 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.     

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 of the black holes under the extended generalized uncertainty principle with linear terms

In this paper, we employ the extended generalized uncertainty principle with linear terms (LEGUP) to investigate the thermodynamics properties of the Schwarzschild and Reissner–Nordström (RN) black holes. Firstly, by constructing the theoretical framework of LEGUP, the minimal temperature of the Schwarzschild black hole and the modified mass–temperature function for the black hole are calculated. Furthermore, the heat capacity function for the Schwarzschild black hole is obtained. After that, we compare LEGUP black hole thermodynamics with EGUP black hole and with the usual forms. Besides, the modification of black hole entropy is discussed, which involves a heuristic analysis of particles absorbed by the black hole. Finally, we derive the LEGUP-corrected temperature, heat capacity and entropy functions of the RN black hole.     

Thermodynamic instability of 3D Einstein-Born-Infeld AdS black holes

Super-entropic black holes possess finite-area but noncompact event horizons and violate the reverse isoperimetric inequality. It has been conjectured that such black holes always have negative specific heat at constant volume \begin{document}$ C_{V} $\end{document} or negative specific heat at constant pressure \begin{document}$ C_{P} $\end{document} whenever \begin{document}$ C_{V}>0 $\end{document}, making them unstable in extended thermodynamics. In this paper, we describe a test of this instability conjecture with a family of nonlinear electrodynamic black holes, namely 3D Einstein-Born-Infeld (EBI) AdS black holes. Our results show that when nonlinear electrodynamics effects are weak, the instability conjecture is valid. However, the conjecture can be violated in some parameter region when nonlinear electrodynamics effects are strong enough. This observation thus provides a counter example to the instability conjecture, which suggests that super-entropic black holes may be thermodynamically stable.     

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 d S 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.     

Spherically symmetric inhomogeneous dust collapse in higher dimensional space-time and cosmic censorship hypothesis

We consider a collapsing spherically symmetric inhomogeneous dust cloud in higher dimensional space-time. We show that the central singularity of collapse can be a strong curvature or a weak curvature naked singularity depending on the initial density distribution.