Phase Structure Of Black Holes Research Articles

Black holes in a cavity: Heat engine and Joule-Thomson expansion

We consider the charged d-dimensional black holes in the cavity in extended phase space and investigate the heat engine and the Joule-Thomson (JT) expansion. Since the phase structure of black holes in the cavity is similar to anti-de-sitter (AdS) cases, we take black holes in a cavity as the working substance in the heat engine and calculate their efficiency in Carnot cycle and rectangular cycle. Also, we discuss whether the JT expansion of charged black holes in the cavity is consistent with AdS cases and find the charged black hole in a cavity always cools down during the isenthalpic process with the decreasing pressure.

Probing phase structure of black holes with Lyapunov exponents

We conjecture that there exists a relationship between Lyapunov exponents and black hole phase transitions. To support our conjecture, Lyapunov exponents of the motion of particles and ring strings are calculated for Reissner-Nordström-AdS black holes. When a phase transition occurs, the Lyapunov exponents become multivalued, and branches of the Lyapunov exponents coincide with black hole phases. Moreover, the discontinuous change in the Lyapunov exponents can be treated as an order parameter, and has a critical exponent of 1/2 near the critical point. Our findings reveal that Lyapunov exponents can be an efficient tool to study phase structure of black holes.

Effects of global monopole on critical behaviors and microstructure of charged AdS black holes

As an intriguing topological defect, global monopole’s influence on behaviors of black holes has always been anticipated but still remains obscure. Analyzing the thermodynamics of charged Anti-de Sitter (AdS) black hole incorporating a global monopole manifests that the black hole undergoes a Van der Waals-like first-order phase transition near the critical point. This paper concentrates on further investigating the transition, aiming at clarifying how the global monopole affects the criticality and microstructure of the charged AdS black holes. As a highlight, this research is implemented by employing new state parameters other than (T, P, V) description and contributes to deeper understanding the rich critical phenomena and phase structure of black holes.

Counterterm method and thermodynamics of hairy black holes in a vector-tensor theory with Abelian gauge symmetry breaking

For a type of nonminimally coupled vector-tensor theories with Abelian gauge symmetry breaking in four-dimensional spacetime and correspondingly asymptotic non-AdS black hole solutions including a cosmological constant, we construct the appropriate boundary terms and derive the associated junction condition. In order to remove the divergences in the stress tensor which is localized on the spacetime boundary, we also involve the suitable surface counterterms into the total action. Using the counterterm method, we calculate the black hole mass. An implicit relation between the black hole carge $Q$ and other parameters is implied by combining the expression of the black hole mass with the first law of black hole thermodynamics. With this implicit relation, we can prove the inequality $Q\ensuremath{\le}M$ which is a general bound for most of charged black holes. Besides, the phase structure of black holes is also investigated in the grand canonical ensemble.

Can shadows reflect phase structures of black holes?

The relation between the black hole shadow and the black hole thermodynamics is investigated. We find that the phase structure can be reflected by the shadow radius for the spherically symmetric black hole. We also find that the shadow size gives correct information but the distortion of the shadow gives wrong information of the phase structure for the axially symmetric black hole.

Q − Φ criticality and microstructure of charged AdS black holes in f(R) gravity

The phase transition and critical behaviors of charged AdS black holes in [Formula: see text] gravity with a conformally invariant Maxwell (CIM) source and constant curvature are further investigated. As a highlight, this research is carried out by employing new state parameters [Formula: see text] and contributes to deeper understanding of the thermodynamics and phase structure of black holes. Our analyses manifest that the charged [Formula: see text]-CIM AdS black hole undergoes a first-order small–large black hole phase transition, and the critical behaviors qualitatively behave like a Van der Waals liquid–vapor system. However, differing from the case in Einstein’s gravity, phase structures of the black holes in [Formula: see text] theory exhibit an interesting dependence on gravity modification parameters. Moreover, we adopt the thermodynamic geometry to probe the black hole microscopic properties. The results show that, on the one hand, both the Ruppeiner curvature and heat capacity diverge exactly at the critical point, on the other hand, the [Formula: see text]-CIM AdS black hole possesses the property as ideal Fermi gases. Of special interest, we discover a microscopic similarity between the black holes and a Van der Waals liquid–vapor system.

Thermodynamic Phase Transition and Critical Behavior of a Spherical Symmetric Black Hole

In this paper, we builded the thermodynamics model of black hole based on the method of York. We obtained the reduced temperature reciprocal function using the action of the system. We studied the phase structure of black holes and Hawking-Page phase transition. We obtained the first order phase transition and critical values of black hole in Rerssner-NordstrOm space time. The results showed that only when two-phase coexistence appeared only when |q| < |qc|.

Non-extended phase space thermodynamics of Lovelock AdS black holes in the grand canonical ensemble

Recently, extended phase space thermodynamics of Lovelock AdS black holes has been of great interest. To provide insight from a different perspective and gain a unified phase transition picture, non-extended phase space thermodynamics of $(n+1)$-dimensional charged topological Lovelock AdS black holes is investigated detailedly in the grand canonical ensemble. Specifically, the specific heat at constant electric potential is calculated and phase transition in the grand canonical ensemble is discussed. To probe the impact of the various parameters, we utilize the control variate method and solve the phase transition condition equation numerically for the case $k=1,-1$. There are two critical points for the case $n=6,k=1$ while there is only one for other cases. For $k=0$, there exists no phase transition point. To figure out the nature of phase transition in the grand canonical ensemble, we carry out an analytic check of the analog form of Ehrenfest equations proposed by Banerjee et al. It is shown that Lovelock AdS black holes in the grand canonical ensemble undergo a second order phase transition. To examine the phase structure in the grand canonical ensemble, we utilize the thermodynamic geometry method and calculate both the Weinhold metric and Ruppeiner metric. It is shown that for both analytic and graphical results that the divergence structure of the Ruppeiner scalar curvature coincides with that of the specific heat. Our research provides one more example that Ruppeiner metric serves as a wonderful tool to probe the phase structures of black holes.

Weinhold geometry and Ruppeiner geometry of black holes with conformal anomaly

The thermodynamic geometry of black holes with conformal anomaly has been investigated in this paper. We study two classical kinds of thermodynamic geometry. Namely, Weinhold geometry and Ruppeiner geometry. It is shown that the condition when Weinhold scalar curvature diverges is the same as the phase transition condition characterized by the divergence of specific heat. It is also shown that Ruppeiner scalar curvature not only reveals the phase structure but also contains the information of Hawking temperature. In a word, both Weinhold metric and Ruppeiner metric can correctly reproduce the phase structure of black holes even when conformal anomaly is taken into consideration.

Phase structure of higher spin black hole

In this paper, we investigate the phase structures of the black holes with one single higher spin hair, focusing specifically on the spin 3 and spin tilde 4 black holes. Based on dimensional analysis and the requirement of having consistent thermodynamics, we derive an universal formula relating the entropy and the conserved charges for arbitrary AdS3 higher spin black holes. Then we use it to study the phase structure of the higher spin black holes. We find that there are six branches of solutions in the spin 3 gravity, eight branches of solutions in the spin tilde 4 gravity and twelve branches of solutions in the G2 gravity. In each case, all branches are related by a simple angle shift in the entropy functions. In the spin 3 case, we reproduce all the results found before. In the spin tilde 4 case, we find that in the low temperature it is at the BTZ branch while in the high temperature it transits to one of two other branches, depending on the signature of the chemical potential, a reflection of charge conjugate asymmetry found before.

Small black holes on cylinders

We find the metric of small black holes on cylinders, i.e. neutral and static black holes with a small mass in d-dimensional Minkowski-space times a circle. The metric is found using an ansatz for black holes on cylinders proposed in hep-th/0204047. We use the new metric to compute corrections to the thermodynamics which is seen to deviate from that of the (d+1)-dimensional Schwarzschild black hole. Moreover, we compute the leading correction to the relative binding energy which is found to be non-zero. We discuss the consequences of these results for the general understanding of black holes and we connect the results to the phase structure of black holes and strings on cylinders.

Phase structure of black holes and strings on cylinders

We use the ( M, n) phase diagram recently introduced in hep-th/0309116 to investigate the phase structure of black holes and strings on cylinders. We first prove that any static neutral black object on a cylinder can be put into an ansatz for the metric originally proposed in hep-th/0204047, generalizing a result of Wiseman. Using the ansatz, we then show that all branches of solutions obey the first law of thermodynamics and that any solution has an infinite number of copies. The consequences of these two results are analyzed. Based on the new insights and the known branches of solutions, we finally present an extensive discussion of the possible scenarios for the Gregory–Laflamme instability and the black hole/string transition.

Gauss-Bonnet black holes in AdS spaces

We study the thermodynamic properties and phase structures of topological black holes in Einstein theory with a Gauss-Bonnet term and a negative cosmological constant. The event horizon of these topological black holes can be a hypersurface with positive, zero, or negative constant curvature. When the horizon is a zero curvature hypersurface, the thermodynamic properties of black holes are completely the same as those of black holes without the Gauss-Bonnet term, although the two black hole solutions are quite different. When the horizon is a negative constant curvature hypersurface, the thermodynamic properties of the Gauss-Bonnet black holes are qualitatively similar to those of black holes without the Gauss-Bonnet term. When the event horizon is a hypersurface with positive constant curvature, we find that the thermodynamic properties and phase structures of black holes drastically depend on the spacetime dimension d and the coefficient of the Gauss-Bonnet term: when $d&gt;~6$, the properties of black holes are also qualitatively similar to the case without the Gauss-Bonnet term, but when $d=5,$ a new phase of locally stable small blacks holes occurs under a critical value of the Gauss-Bonnet coefficient, and beyond the critical value, the black holes are always thermodynamically stable. However, the locally stable small black hole is not globally preferred; instead a thermal anti--de Sitter space is globally preferred. We find that there is a minimal horizon radius, below which the Hawking-Page phase transition will not occur since for these black holes the thermal anti--de Sitter space is always globally preferred.