Gravitational quasi-normal modes of static R~2 Anti-de Sitter black holes

In this paper, we study the gravitational quasi-normal modes(QNMs) for a static R~2 black hole(BH) in Anti-de Sitter(AdS) spacetime. The corresponding master equation of odd parity is derived and the QNMs are evaluated by the Horowitz and Hubeny method. Meanwhile the stability of such BH is also discussed through the temporal evolution of the perturbation field. Here we mainly consider the coefficient λ, which is related to the radius of AdS black hole, on the QNMs of the R~2 AdS BH. The results show that the Re(ω) and |Im(ω)| of the QNMs increase together as |λ| increases for a given angular momentum number l. That indicates with a larger value of |λ| the corresponding R~2 AdS BH returns to stable much more quickly. The dynamic evolution of the perturbation field is consistent with the results derived by the Horowitz and Hubeny method. Since in the conformal field theory the QNMs can reflect its approach to equilibrium, so our related results could be referential to studies of the AdS/CFT conjecture. The relationship between λ and the properties of the static R~2 BH might be helpful for the development of R~2 gravitational theory.     

Fragile black holes

The AdS/CFT correspondence may give a new way of understanding field theories in extreme conditions, as in the quark–gluon plasma phase of quark matter. The correspondence normally involves asymptotically AdS black holes with dual field theories which are defined on locally flat boundary spacetimes; the implicit assumption is that the distortions of spacetime which occur under extreme conditions do not affect the field theory in any unexpected way. However, AdS black holes are [to varying degrees] fragile, in the sense that they become unstable to stringy effects when their event horizons are sufficiently distorted. This implies that field theories on curved backgrounds may likewise be unstable in a suitable sense. We investigate this phenomenon, focussing on the “fragility” of AdS₅ black holes with flat event horizons. We find that, when they are distorted, these black holes are always unstable in string theory. This may have consequences for the detailed structure of the quark matter phase diagram at extreme values of the spacetime curvature.     

Stability of Schwarzschild-AdS for the Spherically Symmetric Einstein-Klein-Gordon System

In this paper, we study the global behavior of solutions to the spherically symmetric coupled Einstein-Klein-Gordon (EKG) system in the presence of a negative cosmological constant. For the Klein-Gordon mass-squared satisfying a ≥ ?1 (the Breitenlohner-Freedman bound being a > ?9/8), we prove that the Schwarzschild-AdS spacetimes are asymptotically stable: Small perturbations of Schwarzschild-AdS initial data again lead to regular black holes, with the metric on the black hole exterior approaching, at an exponential rate, a Schwarzschild-AdS spacetime. The main difficulties in the proof arise from the lack of monotonicity for the Hawking mass and the asymptotically AdS boundary conditions, which render even (part of) the orbital stability intricate. These issues are resolved in a bootstrap argument on the black hole exterior, with the redshift effect and weighted Hardy inequalities playing the fundamental role in the analysis. Both integrated decay and pointwise decay estimates are obtained. As a corollary of our estimates on the Klein-Gordon field, one obtains in particular exponential decay in time of spherically-symmetric solutions to the linear Klein-Gordon equation on Schwarzschild-AdS.     

Thermodynamics of Hořava–Lifshitz black holes

We study black holes in the Ho?ava–Lifshitz gravity with a parameter λ. For 1/3≤λ<3, the black holes behave the Lifshitz black holes with dynamical exponent 0<z≤4, while for λ>3, the black holes behave the Reissner–Nordström type black hole in asymptotically flat spacetimes. Hence, these all are quite different from the Schwarzschild–AdS black hole of Einstein gravity. The temperature, mass, entropy, and heat capacity are derived for investigating thermodynamic properties of these black holes.     

Anisotropic conformal infinity

We generalize Penrose’s notion of conformal infinity of spacetime, to situations with anisotropic scaling. This is relevant not only for Lifshitz-type anisotropic gravity models, but also in standard general relativity and string theory, for spacetimes exhibiting a natural asymptotic anisotropy. Examples include the Lifshitz and Schrödinger spaces (proposed as AdS/CFT duals of nonrelativistic field theories), warped AdS ₃, and the near-horizon extreme Kerr geometry. The anisotropic conformal boundary appears crucial for resolving puzzles of holographic renormalization in such spacetimes.     

Scalar field coupling to Einstein tensor in regular black hole spacetime

In this paper, we study the perturbation property of a scalar field coupling to Einstein’s tensor in the background of the regular black hole spacetimes. Our calculations show that the the coupling constant \(\eta \) imprints in the wave equation of a scalar perturbation. We calculated the quasinormal modes of scalar field coupling to Einstein’s tensor in the regular black hole spacetimes by the 3rd order WKB method.     

Quasinormal Modes for Electromagnetic Field Perturbation of the Asymptotic Safe Black Hole

In this paper, the quasinormal modes (QNMs) of electromagnetic field perturbation to asymptotic safe (AS) black hole are discussed. Through six-order WKB approach we investigate the effects of quantum correction to the quasinormal modes (QNMs) numerically. Meanwhile by means of finite difference method, the evolutions of such perturbation to the safe black hole are figured out with corresponding parameters. It is found that the stability of black hole remains although the decay frequency and damping speed of oscillations are respectively increased and lowered by the quantum correction to classic Schwarzschild black hole.     

Analytic phase structures and thermodynamic curvature for the charged AdS black hole in alternative phase space

In this paper, we visit the thermodynamic criticality and thermodynamic curvature of the charged AdS black hole in a new phase space. It is shown that when the square of the total charge of the charged black hole is considered as a thermodynamic quantity, the charged AdS black hole also admits a van der Waals-type critical behavior without the help of thermodynamic pressure and thermodynamic volume. Based on this, we study the fine phase structures of the charged AdS black hole with fixed AdS background in the new framework. On the one hand, we give the phase diagram structures of the charged AdS black hole accurately and analytically, which fills up the gap in dealing with the phase transition of the charged AdS black holes by taking the square of the charge as a thermodynamic quantity. On the other hand, we analyse the thermodynamic curvature of the black hole in two coordinate spaces. The thermodynamic curvatures obtained in two different coordinate spaces are equivalent to each other and are also positive. Based on an empirical conclusion under the framework of thermodynamic geometry, we speculate that when the square of charge is treated as an independent thermodynamic quantity, the charged AdS black hole is likely to present a repulsive between its molecules. More importantly, based on the thermodynamic curvature, we obtain a universal exponent at the critical point of phase transition.     

f(R) Black Holes as Heat Engines

With the cosmological constant considered as a thermodynamic variable in the extended phase space, it is natural to study the thermodynamic cycles of the black hole, which is conjectured to be performed using renormalization group flow. We first investigate the thermodynamic cycles of a 4-dimensional asymptotically AdS f(R) black hole. Then we study the thermodynamic cycles of higher dimensional asymptotically AdS f(R) black holes. It is found that when ΔV ? ΔP, the efficiency of isobar-isochore cycles running between high temperature T_H and low temperature T_C will increase to its maximum value, which is exactly the Carnot cycles’ efficiency both in 4-dimensional and in higher dimensional cases. We speculate that this property is universal for AdS black holes, if there is no phase transition in the thermodynamic cycle. This result may deepen our understanding of the thermodynamics of the AdS black holes.     

Signature of Different Phases of Ricci Flat Black Holes and AdS Solitons in Gauss-Bonnet Gravity

From the perturbation around the background spacetimes in the Gauss-Bonnet gravity, we find the physical evidence that Ricci flat AdS black holes and AdS solitons are different physical configurations and stay in different phases, this serves as a strong support to the previous mathematical and thermodynamical arguments.     

Maxwell’s equal area law for black holes in power Maxwell invariant

In this paper, we consider the phase transition of black hole in power Maxwell invariant by means of Maxwell’s equal area law. First, we review and study the analogy of nonlinear charged black hole solutions with the Van der Waals gas–liquid system in the extended phase space, and obtain isothermal P-v diagram. Then, using the Maxwell’s equal area law we study the phase transition of AdS black hole with different temperatures. Finally, we extend the method to the black hole in the canonical (grand canonical) ensemble in which charge (potential) is fixed at infinity. Interestingly, we find the phase transition occurs in the both ensembles. We also study the effect of the parameters of the black hole on the two-phase coexistence. The results show that the black hole may go through a small-large phase transition similar to those of usual non-gravity thermodynamic systems.     

The AdS5 Black Hole Space-time with the Perturbed?Dilaton Field Background

The AdS ₅ black hole space-time with perturbed dilaton field background considered. We use the holographic AdS/QCD soft-wall model to investigate the wave functions and the effective potential. In this model, glueballs are described by a massless scalar field in an AdS ₅ black hole with a dilaton soft-wall background. For the first time we use modified dilaton field and discuss the consequence of the perturbation. In order to obtain the effective potential we rewrite the equation of motion in the Schr?dinger like equation, then try to find corresponding solution.     

On the Geometry and Mass of Static,Asymptotically AdS Spacetimes,and the Uniqueness of the AdS Soliton

We prove two theorems, announced in [6], for static spacetimes that solve Einstein's equation with negative cosmological constant. The first is a general structure theorem for spacetimes obeying a certain convexity condition near infinity, analogous to the structure theorems of Cheeger and Gromoll for manifolds of non-negative Ricci curvature. For spacetimes with Ricci-flat conformal boundary, the convexity condition is associated with negative mass. The second theorem is a uniqueness theorem for the negative mass AdS soliton spacetime. This result lends support to the new positive mass conjecture due to Horowitz and Myers which states that the unique lowest mass solution which asymptotes to the AdS soliton is the soliton itself. This conjecture was motivated by a nonsupersymmetric version of the AdS/CFT correspondence. Our results add to the growing body of rigorous mathematical results inspired by the AdS/CFT correspondence conjecture. Our techniques exploit a special geometric feature which the universal cover of the soliton spacetime shares with familiar ``ground state' spacetimes such as Minkowski spacetime, namely, the presence of a null line, or complete achronal null geodesic, and the totally geodesic null hypersurface that it determines. En route, we provide an analysis of the boundary data at conformal infinity for the Lorentzian signature static Einstein equations, in the spirit of the Fefferman-Graham analysis for the Riemannian signature case. This leads us to generalize to arbitrary dimension a mass definition for static asymptotically AdS spacetimes given by Chruciel and Simon. We prove equivalence of this mass definition with those of Ashtekar-Magnon and Hawking-Horowitz.     

Three-dimensional massive Kiselev AdS black hole and its thermodynamics

We present an exact three-dimensional massive Kiselev AdS black hole solution. This Kiselev black hole is neither perfectly fluid, nor is it the quintessential solution, but the BTZ black hole modified by the anisotropic matter. This black hole possesses an essential singularity at its radial origin and a single horizon whose radius will increase monotonically when the parameter of the anisotropic matter field ω decreases. We calculate all thermodynamic quantities and find that the first law of thermodynamics of this massive Kiselev AdS black hole can be protected, while the consistent Smarr formula is only held in the extended thermodynamic phase space. After examining the sign of free energy, we conclude that there is no Hawking-Page transition since the massive Kiselev AdS black hole phase is always thermodynamically favored. Moreover, we study the phase transition between the Kiselev AdS black hole and BTZ black hole by considering the matchings for their temperature. We find that the Kiselev AdS black hole is still a thermodynamically more preferred phase, because it always has a smaller amount of free energy than the BTZ black hole, which seems to indicate that the anisotropic matter field may emerge naturally in BTZ black hole spacetime under some thermal fluctuations. We also show a first order phase transition between the Kiselev AdS black hole phase with -1w -1/2 and the black hole phase with -1/2w0. As the Kiselev AdS black hole has some notable features on the phase transition of black holes in three dimensions, it provides important clues to further investigate these both surprising and similar behaviors in four and higher dimensions.     

Geometrothermodynamics of Van der Waals black hole

We study the geometrothermodynamics of a special asymptotically AdS black hole, i.e. Van der Waals \(\left( VdW\right) \) black hole, in the extended phase space where the negative cosmological constant \(\Lambda \) can be regarded as thermodynamic pressure. Analysing some special conditions of this black hole with geometrothermodynamical method, we find a good correlation with ordinary cases according to the state equation.     

Holographic screening length in a hot plasma of two sphere

We study the screening length \(L_{\mathrm{max}}\) of a moving quark–antiquark pair in a hot plasma, which lives in a two sphere, \(S^2\), using the AdS/CFT correspondence in which the corresponding background metric is the four-dimensional Schwarzschild–AdS black hole. The geodesic of both ends of the string at the boundary, interpreted as the quark–antiquark pair, is given by a stationary motion in the equatorial plane by which the separation length L of both ends of the string is parallel to the angular velocity \(\omega \). The screening length and total energy H of the quark–antiquark pair are computed numerically and show that the plots are bounded from below by some functions related to the momentum transfer \(P_c\) of the drag force configuration. We compare the result by computing the screening length in the reference frame of the moving quark–antiquark pair, in which the background metrics are “Boost-AdS” and Kerr–AdS black holes. Comparing both black holes, we argue that the mass parameters \(M_{\mathrm{Sch}}\) of the Schwarzschild–AdS black hole and \(M_{\mathrm{Kerr}}\) of the Kerr–AdS black hole are related at high temperature by \(M_{\mathrm{Kerr}}=M_{\mathrm{Sch}}(1-a^2l^2)^{3/2}\), where a is the angular momentum parameter and l is the AdS curvature.     

Notes on Black Hole Phase Transitions

In these notes we present a summary of existing ideas about phase transitions of black hole spacetimes in semiclassical gravity and offer some thoughts on three possible scenarios or mechanisms by which these transitions could take place. We begin with a review of the thermodynamics of a black hole system and emphasize that the phase transition is driven by the large entropy of the black hole horizon. Our first theme is illustrated by a quantum atomic black hole system, generalizing to finite-temperature a model originally offered by Bekenstein. In this equilibrium atomic model, the black hole phase transition is realized as the abrupt excitation of a high energy state, suggesting analogies with the study of two-level atoms. Our second theme argues that the black hole system shares similarities with the defect-mediated Kosterlitz–Thouless transition in condensed matter. These similarities suggest that the black hole phase transition may be more fully understood by focusing upon the dynamics of black holes and white holes, the spacetime analogy of vortex and antivortex topological defects. Finally, we compare the black hole phase transition to another transition driven by an (exponentially) increasing density of states, the Hagedorn transition first found in hadron physics in the context of dual models or the old string theory. In modern string theory the Hagedorn transition is linked by the Maldacena conjecture to the Hawking–Page black hole phase transition in Anti-de Sitter (AdS) space, as observed by Witten. Thus, the dynamics of the Hagedorn transition may yield insight into the dynamics of the black hole phase transition. We argue that characteristics of the Hagedorn transition are already contained within the dynamics of classical string systems. Our third theme points to carrying out a full nonperturbative and nonequilibrium analysis of the large N behavior of classical SU(N) gauge theories to understand its Hagadorn transition. By invoking the Maldacena conjecture we can then gain valuable insight into black hole phase transitions in AdS space.     

Fragile black holes and an angular momentum cutoff in peripheral heavy ion collisions

In collisions of heavy ions at extremely high energies, it is possible for a significant quantity of angular momentum to be deposited into the Quark–Gluon Plasma which is thought to be produced. We develop a simple geometric model of such a system, and show that it is dual, in the AdS/CFT sense, to a rotating AdS black hole with a topologically planar event horizon. However, when this black hole is embedded in string theory, it proves to be unstable, for all non-zero angular momenta, to a certain non-perturbative effect: the familiar planar black hole, as used in most AdS/CFT analyses of QGP physics, is “fragile”. The upshot is that the AdS/CFT duality apparently predicts that the QGP should always become unstable when it is produced in peripheral collisions. However, we argue that holography indicates that relatively low angular momenta delay the development of the instability, so that in practice it may be observable only for peripheral collisions involving favorable impact parameters, generating extremely large angular momenta. In principle, the result may be holographic prediction of a cutoff for the observable angular momenta of the QGP, or perhaps of an analogous phenomenon in condensed matter physics.