Phase Transition Of Black Holes Research Articles

Phase transitions in charged topological black holes dressed with a scalar hair

Phase transitions in charged topological black holes dressed with a scalar field are studied. These black holes are solutions of the Einstein-Maxwell theory with a negative cosmological constant and a conformally coupled real self-interacting scalar field. Comparing, in the grand canonical ensemble, the free energies of the hairy and undressed black holes two different phase transitions are found. The first of them is one of second-order type and it occurs at a temperature defined by the value of the cosmological constant. Below this temperature an undressed black hole spontaneously acquires a scalar hair. The other phase transition is one of first-order type. The corresponding critical temperature, which is bounded from above by the one of the previous case, strongly depends on the coupling constant of the quartic self-interaction potential, and this transition only appears when the coupling constant is less than a certain value. In this case, below the critical temperature the undressed black is thermodynamically favored. However, when the temperature exceeds the critical value a hairy black hole is likely to be occur.

Glassy phase transition and stability in black holes

Black hole thermodynamics, confined to the semi-classical regime, cannot address the thermodynamic stability of a black hole in flat space. Here we show that inclusion of correction beyond the semi-classical approximation makes a black hole thermodynamically stable. This stability is reached through a phase transition. By using Ehrenfest's scheme we further prove that this is a glassy phase transition with a Prigogine-Defay ratio close to 3. This value is well placed within the desired bound (2 to 5) for a glassy phase transition. Thus our analysis indicates a very close connection between the phase transition phenomena of a black hole and glass forming systems. Finally, we discuss the robustness of our results by considering different normalisations for the correction term.

Signature of the black hole phase transition in quasinormal modes

We study the perturbation of the scalar field interacting with the Maxwell field in the background of d-dimensional charged AdS black hole and AdS soliton. Different from the single classical field perturbation, which always has the decay mode in the black hole background, we observe the possible growing mode when the perturbation of the scalar field strongly couples to the Maxwell field. Our results disclose the signature of how the phase transition happens when the interaction among classical fields is strong. The sudden change of the perturbation to growing mode is also observed in the AdS soliton with electric potential. However in the magnetic charged AdS soliton background, we observe the consistent perturbation behavior when the interaction between scalar field and Maxwell field is considered. This implies that for the magnetic charged AdS soliton configuration, unlike the situation with electric potential, there is no scalar field condensation which causes the phase change.

Holographic superconductors with Hořava-Lifshitz black holes

We discuss the phase transition of planar black holes in Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz gravity by introducing a Maxwell field and a complex scalar field. We calculate the condensate of the charged operators in the dual conformal field theories when the mass square of the complex scalar field is ${m}^{2}=\ensuremath{-}2/{L}^{2}$ and ${m}^{2}=0$, respectively. We compute the electrical conductivity of the Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz superconductor in the probe approximation. In particular, it is found that there exists a spike in the conductivity for the case of the operator with scaling dimension one. These results are quite similar to those in the case of Schwarzschild-AdS black holes, which demonstrates that the holographic superconductivity is a robust phenomenon associated with asymptotic AdS black holes.

Phase Transition for Scalar and Topological Black Holes

Phase Transition for Scalar and Topological Black Holes

Thermodynamics of dilaton-axion black holes

Considering a generalized action for the Einstein-Maxwell theory in four dimensions coupled to scalar and pseudoscalar fields, the thermodynamic properties of asymptotically flat black hole solutions in such a background are investigated. Bekenstein-Hawking area-entropy law is verified for these class of black holes. From the property of specific heat, it is shown that such black holes can be stable for a certain choice of the parameters like charge, mass, and the scalar vacuum expectation value. The possibility of a black hole phase transition is discussed in this context.

Thermodynamics and phase transitions in the Born-Infeld-anti-de Sitter black holes

We investigate the Born-Infeld--anti--de Sitter (BIAdS) black hole solutions in the four dimensions, which is a nonlinear generalization of the Reissner-Norstr\om-AdS (RNAdS) black hole. We analyze all thermodynamic quantities of the BIAdS black hole in the canonical ensembles, which are characterized by the charge $Q$, the mass $M$, the nonlinear parameter $b$, comparing with those of the RNAdS and Schwarzschild-AdS black hole. We find the forbidden region of $0\ensuremath{\le}bQl0.5$ for the presence of a charged BIAdS black hole. We also discuss the Hawking-Page phase transitions in the BIAdS black holes. Here we obtain a new Hawking-Page phase transition for the $bQ=0.5$ critical BIAdS black hole.

Phase Transitions of Charged Kerr-AdS Black Holes from Large-N Gauge Theories

We study N = 4 super Yang-Mills theories on a three-sphere with two types of chemical potential. One is associated with the R-symmetry and the other with the rotational symmetry of S 3 (SO(4) symmetry). These correspond to charged Kerr-AdS black holes via AdS/CFT. The exact partition functions at zero coupling are computed and the thermodynamical properties are studied. We find a nontrivial gap between the confinement/deconfinement transition line and the boundary of the phase diagram when we include more than four chemical potentials. In dual gravity, we find such a gap in the phase diagram by studying the thermodynamics of the charged Kerr-AdS black hole. This shows that the qualitative phase structures agree between both theories. We also find that the ratio between the thermodynamical quantities is close to well-known factor of 3/4 even at low temperatures.

Correction value to charged Bekenstein-Hawking black hole entropy

Recently, based on the study of black hole Hawking radiation with the tunnel effect method, we found that the radiation spectrum of the black hole is not a strict pure thermal spectrum. It is a very interesting problem to determine how the departure of the black hole radiation spectrum from the pure thermal spectrum affects entropy. We calculate the partition function by the energy spectrum obtained using tunnel effect. Using the relation between the partition function and entropy, we derive the correction value to Bekenstein-Hawking entropy of the charged black hole. Furthermore, we obtain the conditions that various thermodynamic quantities must satisfy, when phase transition of the charged black hole occurs.

Thermodynamic curvature and phase transitions in Kerr-Newman black holes

Singularities in the thermodynamics of Kerr-Newman black holes are commonly associated with phase transitions. However, such interpretations are complicated by a lack of stability and, more significantly, by a lack of conclusive insight from microscopic models. Here, I focus on the later problem. I use the thermodynamic Riemannian curvature scalar $R$ as a try to get microscopic information from the known thermodynamics. The hope is that this could facilitate matching black hole thermodynamics to known models of statistical mechanics. For the Kerr-Newman black hole, the sign of $R$ is mostly positive, in contrast to that for ordinary thermodynamic models, where $R$ is mostly negative. Cases with negative $R$ include most of the simple critical point models. An exception is the Fermi gas, which has positive $R$. I demonstrate several exact correspondences between the two-dimensional Fermi gas and the extremal Kerr-Newman black hole. Away from the extremal case, $R$ diverges to $+\ensuremath{\infty}$ along curves of diverging heat capacities ${C}_{J,\ensuremath{\Phi}}$ and ${C}_{\ensuremath{\Omega},Q}$, but not along the Davies curve of diverging ${C}_{J,Q}$. Finding statistical mechanical models with like behavior might yield additional insight into the microscopic properties of black holes. I also discuss a possible physical interpretation of $|R|$.

Phase transitions in charged topological-AdS black holes

We study the perturbative behaviour of charged topological-AdS black holes. We calculate both analytically and numerically the quasi-normal modes of the electromagnetic and gravitational perturbations. Keeping the charge-to-mass ratio constant, we show that there is a second-order phase transition at a critical temperature at which the mass of the black hole vanishes. We pay special attention to the purely dissipative modes appearing in the spectrum as they behave singularly at the critical point.

Unified geometric description of black hole thermodynamics

In the space of thermodynamic equilibrium states we introduce a Legendre invariant metric which contains all the information about the thermodynamics of black holes. The curvature of this thermodynamic metric becomes singular at those points where, according to the analysis of the heat capacities, phase transitions occur. This result is valid for the Kerr-Newman black hole and all its special cases and, therefore, provides a unified description of black hole phase transitions in terms of curvature singularities.

Phase transition for black holes with scalar hair and topological black holes

We study phase transitions between black holes with scalar hair and topological black holes in asymptotically anti-de Sitter spacetimes. As the ground state solutions, we introduce the non-rotating BTZ black hole in three dimensions and topological black hole with hyperbolic horizon in four dimensions. For the temperature matching only, we show that the phase transition between black hole with scalar hair (Martinez–Troncoso–Zanelli black hole) and topological black hole is second-order by using differences between two free energies. However, we do not identify what order of the phase transition between scalar and non-rotating BTZ black holes occurs in three dimensions, although there exists a possible decay of scalar black hole to non-rotating BTZ black hole.

Canonical Entropy of Black Hole in the Generalized Uncertainty Principle

Recently, there has been much attention devoted to resolving the quantum corrections to the Bekenstein-Hawking black hole entropy. In particular, many researchers have expressed a vested interest in the coefficient of the logarithmic term of the black hole entropy correction term. In this paper, based on the correction to black hole thermodynamic quantity due to the generalized uncertainty principle, we calculate the partition function by energy spectrum obtained using tunneling effect. Furthermore we derive the black hole entropy. In the expression, we not only consider the generalized uncertainty principle but also consider the departure of black hole radiation spectrum from pure thermal spectrum. According to criterion law of thermodynamic systems phase transition, we discuss the phase transition of AdS black hole and derive that the phase transition of AdS black hole is a secondary one.

Hawking-Page phase transition of black Dp-branes and R-charged black holes with an IR cutoff

We show that the confinement-deconfinement phase transition of supersymmetric Yang-Mills theories with 16 supercharges in various dimensions can be realized through the Hawking-Page phase transition between the near horizon geometries of black Dp-branes and BPS Dp-branes by removing a small radius region in the geometry in order to realize a confinement phase, which generalizes the Herzog's discussion for the holographic hard-wall AdS/QCD model. Removing a small radius region in the gravitational dual corresponds to introducing an IR cutoff in the dual field theory. We also discuss the Hawking-Page phase transition between thermal $AdS_5$, $AdS_4$, $AdS_7$ spaces and R-charged AdS black holes coming from the spherical reduction of the decoupling limit of rotating D3-, M2-, and M5- branes in type IIB supergravity and 11 dimensional supergravity in grand canonical ensembles, where the IR cutoff also plays a crucial role in the existence of the phase transition.

The phase transition and the quasi-normal modes of black holes

We reexamined the argument that the quasinormal modes could be a probe of the phase transition of a topological black hole to a hairy configuration by investigating general scalar perturbations. We found further evidence in the quasinormal modes for this phase transition. For the general black hole configurations, we observed that although the quasinormal modes can present us different phases of different configurations, there is no dramatic change in the slope of quasinormal frequencies at the critical point of the phase transition. More detailed studies of quasinormal modes are needed to reveal the subtle behavior of the phase transition.

Quasinormal modes and phase transition of black holes

We have studied the scalar field as well as the fermionic field perturbations in the background of the massless BTZ black holes. Comparing with the perturbation results in the generic non-rotating BTZ black hole background, we found that the massless BTZ hole contains only normal modes in the perturbations. We argued that this special property reflects that the massless BTZ black hole is a different phase from that of the generic non-rotating BTZ hole.

Canonical entropy and phase transition of black hole

摘要 应用隧道效应对黑洞Hawking辐射研究得到的辐射谱,对非旋转黑洞的正则熵进行讨论.所得熵遵守Bekenstein-Hawking 面积定律,并带有修正项,主要修正项与面积的对数成正比,另有与黑洞热容量有关的修正项.利用所给出的正则熵,对黑洞的相变进行讨论,得到当黑洞的热容量出现发散时,正则熵在该处并不出现复数,由此认为此相变为二级相变. 关键词: 正则系综 / 量子修正 / 黑洞相变 Abstract By applying the radiation spectrum obtained from tunnel effect, we obtain the normal canonical entropy of black hole by discussing the entropy of non-rotation black hole. The entropy satisfies the Bekenstein-Hawking area law, and contains the terms of correction whose main terms are proportional to the logarithm of the area, and the rest of the correction terms are related to the thermal capacity of black hole. With the help of the obtained normal canonical entropy, we studied the phase transition and showed that when the thermal capacity is emanative, there are no plural numbers at this point in the normal canonical entropy, which shows that the phase transition is of the second order. Keywords: canonical ensemble / quantum correction / phase transition of black hole 作者及机构信息 赵 仁, 张丽春, 张胜利 基金项目: 山西省自然科学基金(批准号:2006011012)资助的课题. Authors and contacts 参考文献 施引文献

Towers of gravitational theories

In this essay we introduce a theoretical framework designed to describe black hole dynamics. The difficulties in understanding such dynamics stems from the proliferation of scales involved when one attempts to simultaneously describe all of the relevant dynamical degrees of freedom. These range from the modes that describe the black hole horizon, which are responsible for dissipative effects, to the long wavelength gravitational radiation that drains mechanical energy from macroscopic black hole bound states. We approach the problem from a Wilsonian point of view, by building a tower of theories of gravity each of which is valid at different scales. The methodology leads to multiple new results in diverse topics including phase transitions of Kaluza-Klein black holes and the interactions of spinning black hole in non-relativistic orbits. Moreover, our methods tie together speculative ideas regarding dualities for black hole horizons to real physical measurements in gravitational wave detectors.

Quasi-normal modes of electromagnetic perturbations of four-dimensional topological black holes with scalar hair

We study the perturbative behaviour of topological black holes with scalar hair. We calculate both analytically and numerically the quasi-normal modes of the electromagnetic perturbations. In the case of small black holes we find evidence of a second-order phase transition of a topological black hole to a hairy configuration.