本文研究了具有等角动量的Kerr-AdS_5 × S^5时空的引力微扰。在这个时空中，我们发现了两种经典不稳定性，超辐射不稳定性和Gregory-Laflamme不稳定性。超辐射不稳定性是由超辐射引起的波放大和由于AdS时空的势垒引起的波反射引起的。格雷戈里-拉弗拉姆不稳定性出现在内部空间S^5的卡鲁扎-克莱因模中，破坏了对称性SO（6）。考虑到这些不稳定性，我们揭示了Kerr-AdS_5 x S^5时空的相结构。AdS/CFT对应的含义进行了讨论。
英文摘要：
We study gravitational perturbations of the Kerr-AdS_5 x S^5 spacetime with equal angular momenta. In this spacetime, we found the two kinds of classical instabilities, superradiant and Gregory-Laflamme instabilities. The superradiant instability is caused by the wave amplification via superradiance, and by wave reflection due to the potential barrier of the AdS spacetime. The Gregory-Laflamme instability appears in Kaluza-Klein modes of the internal space S^5 and breaks the symmetry SO(6). Taken into account these instabilities, the phase structure of Kerr-AdS_5 x S^5 spacetime is revealed. The implication for the AdS/CFT correspondence is also discussed.
In this paper, we study Joule-Thomson expansion for Kerr-AdS black holes in the extended phase space. Joule-Thomson expansion formula of Kerr-AdS black holes is derived. We investigate both isenthalpic and numerical inversion curves in the T-P plane and demonstrate the cooling-heating regions for Kerr-AdS black holes. We also calculate the ratio between minimum inversion and critical temperatures for Kerr-AdS black holes.
We find that the Kerr-(Newman)-AdS$_4$ black hole will be shadowless if its rotation parameter is larger than a critical value and the shadowless-ness may be related to the appearance of the null hypersurface caustics (NHC) both inside the Cauchy horizon and outside the event horizon for the black hole with the rotation parameter beyond the critical value. Our studies also further confirm that whether an ultraspinning black hole is super-entropic or not is unrelated to the existence of the NHC outside the event horizon.
Black hole thermodynamics of the Kerr-AdS spacetime in three-dimensional general relativity is analyzed using a Hamiltonian approach. The values of the conserved charges and entropy, obtained by a proper treatment of the AdS asymptotic conditions, are shown to satisfy the first law of black hole dynamics.
We numerically explore the structure of quasi-normal (QN) frequencies of the five-dimensional small and large Kerr-anti de Sitter (Kerr-AdS${}_5$) black hole with equal and unequal rotations. Our investigation also covers low and high Hawking temperatures. We then study the stability of the Kerr-AdS${}_5$ black hole and the structure of highly damped QN modes, which would reflect the thermodynamic property of the Kerr-AdS${}_5$ black hole. We find that the highly damped complex QN frequencies of a nearly maximally spinning Kerr-AdS${}_5$ black hole have the periodic separation of the surface g…
A general Hamiltonian approach to black hole thermodynamics is used to study entropy and conserved charges for Kerr-AdS solutions in general relativity. These thermodynamic variables are first consistently defined by choosing suitable boundary conditions, and then, they are shown to satisfy the first law of black hole dynamics
In the previous work we give a microscopic explanation of the entropy for the BTZ black hole and four-dimensional Kerr black hole based on the massless scalar field theory on the horizon. An essential input is the central charges of those black holes. In this paper, we calculate the central charges for Kerr black holes and Kerr-AdS black holes in diverse dimensions by rewriting the entropy formula in a suggesting way. Then we also give the statistical explanation for the entropy of those black holes based on the scalar field on the horizon which similar to 4D kerr black hole.
We find generators of the conformal symmetry for the class of Kerr-Newman-NUT-AdS black holes from the deformed scalar probe equation. We find two classes of solutions for the generators (also known as conformal J and Q pictures). The two classes of deformed generators are the extension of similar generators for the regular conformal symmetry. Moreover, we find that the two pictures can be generalized and extended into a general picture. In each picture, the generators produce an extended local family of SL(2,R)_L \times SL(2,R)_R hidden conformal symmetries for the Kerr-Newman-NUT-AdS black h…
The canonical approach to black hole entropy in Poincaré gauge theory without matter is extended to include Maxwell field as a matter source. The new formalism is used to calculate asymptotic charges and entropy of Kerr--Newmann--AdS black holes with torsion. The result implies that the first law, with a nontrivial contribution of the Maxwell field, takes the same form as in general relativity.
Using a Hamiltonian approach, we introduce black hole entropy for Kerr-AdS spacetimes with torsion as the canonical charge on horizon. In spite of a completely different geometric setting with respect to GR, the resulting thermodynamic variables, energy, angular momentum and entropy, are shown to be proportional to the corresponding GR expressions. The validity of the first law is confirmed.
Combining with the small-large black hole phase transition, the thermodynamic geometry has been well applied to study the microstructure for the charged AdS black hole. In this paper, we extend the geometric approach to the rotating Kerr-AdS black hole and aim to develop a general approach for the Kerr-AdS black hole. Treating the entropy and pressure as the fluctuation coordinates, we construct the Ruppeiner geometry for the Kerr-AdS black hole by making the use of the Christodoulou-Ruffini-like squared-mass formula, which is quite different from the charged case. Employing the empirical obse…
We explore some (especially, thermodynamical) properties of the dyonic Kerr-Sen-AdS$_4$ black hole and its ultraspinning counterpart, and check whether or not both black holes satisfy the first law and Bekenstein-Smarr mass formulas. To this end, new Christodoulou-Ruffini-like squared-mass formulae for the usual dyonic Kerr-Sen-AdS$_4$ solution and its ultraspinning cousin are deduced. Similar to the ultraspinning Kerr-Sen-AdS$_4$ black hole case, we demonstrate that the ultraspinning dyonic Kerr-Sen-AdS$_4$ black hole does not always violate the reverse isoperimetric inequality (RII) since th…
Black hole spacetimes asymptotic to five-dimensional anti-de Sitter spacetime are of great interest in connection with the string-gauge duality. In the rotating case, such black holes tend to become unstable, in several different ways, if their specific angular momenta fall in certain ranges. Here we consider the well-known Emparan-Myers fragmentation instability for singly rotating AdS$_5$-Kerr black holes, paying particular attention to the case where the specific angular momentum exceeds the asymptotic AdS$_5$ curvature length scale.
Classical Censorship permits AdS$_5$-Kerr black holes with arbitrarily large angular momenta per unit mass, which does not seem reasonable from a holographic point of view. However, it has been shown that, when these black holes are embedded in string theory, their angular momentum per unit mass is in fact bounded by $2\sqrt{2}L$, where $L$ is the asymptotic curvature scale. One might suppose that the most rapidly rotating AdS$_5$-Kerr black holes, with angular momentum per unit mass close to this bound, might be unstable, for example, to a superradiant instability. We show that this is not al…
We show the generic non-extremal Kerr-Newman-NUT-AdS black holes are holographically dual to the hidden conformal field theories in two different pictures. The two pictures can be merged together to the dual CFTs in general picture, that are generated by the $SL(2,\mathbb{Z})$ modular group. We also extend the calculation to the extremal limit and find the corresponding quantities. Using the extended central charges from the Kerr/CFT correspondence, we also find agreement between the macroscopic and microscopic entropies. We also find the absorption cross-section of the scalar probes for the g…
We show that the Hawking temperature is modified in the presence of dark energy in an emergent gravity scenario for Kerr-Newman(KN) and Kerr-Newman-AdS(KNAdS) background metrics. The emergent gravity metric is not conformally equivalent to the gravitational metric. We calculate the Hawking temperatures for these emergent gravity metrics along $θ=0$. Also we show that the emergent black hole metrics are satisfying Einstein's equations for large $r$ and $θ=0$. Our analysis is done in the context of dark energy in an emergent gravity scenario having $k-$essence scalar fields $ϕ$ with a Dirac-Born…
It has been recently observed that a scalar field with Robin boundary conditions (RBCs) can trigger both a superradiant and a bulk instability for a BTZ black hole (BH). To understand the generality and scrutinize the origin of this behavior, we consider here the superradiant instability of a Kerr BH confined either in a mirror-like cavity or in AdS space, triggered also by a scalar field with RBCs. These boundary conditions are the most general ones that ensure the cavity/AdS space is an isolated system, and include, as a particular case, the commonly considered Dirichlet boundary conditions …
We present new analytic rotating AdS$_4$ black holes, found as solutions of 4d gauged $\mathcal{N}=2$ supergravity coupled to abelian vector multiplets with a symmetric scalar manifold. These configurations preserve two real supercharges and have a smooth limit to the BPS Kerr-Newman-AdS$_4$ black hole. We spell out the solution of the $STU$ model admitting an uplift to M-theory on S$^7$. We identify an entropy function, which upon extremization gives the black hole entropy, to be holographically reproduced by the leading $N$ contribution of the generalized superconformal index of the dual the…
We study hidden symmetries, the symmetries associated with the Killing tensors, of the near horizon geometry of odd-dimensional Kerr-AdS-NUT black hole in two limits: generic extremal and extremal vanishing horizon (EVH) limits. Starting from Kerr-AdS-NUT black hole in ellipsoidal coordinates which admits integrable geodesic equations, we obtain the near horizon extremal/EVH geometries and their principal and Killing tensors by taking the near horizon limit. We explicitly demonstrate that geodesic equations are separable and integrable on theses near horizon geometries. We also compute the con…
The gravitational collapse in asymptotically AdS spacetimes is studied, using the differential configurational entropy (DCE). The DCE is shown to comply with the instability of the Einstein-Klein-Gordon system, leading to different stages in the route to turbulence and final black hole formation, including near the critical behavior.
We use the continued fraction method to determine the eigenfrequencies associated with a scalar field around a Kerr-like black hole. The Kerr-like metric considered in this article is a subclass of the general parametrization of axisymmetric black holes proposed by Konoplya, Rezzolla and Zhidenko. In addition to its mass $M$ and specific angular momentum $a$, the black hole depends on a third parameter $η$, called the deformation parameter. We investigate how the deformation parameter affects the quasinormal modes and the quasibound states of a massive scalar field around the black hole. In pa…
In theories of gravity where the cosmological constant defines a thermodynamic variable, the pressure, it has been shown that solutions of Einstein's equations have a corresponding thermodynamic volume. In general, the expression for the volume is not the same as the one arising from naive geometrical considerations. Both rotation and nut charge are properties known in the literature to give non-geometric thermodynamic volumes, and so we combine the two in a single example and compute the volume for the Kerr-bolt-AdS spacetime, presenting a new expression that generalizes the previously known …
We show that the linear perturbations of any spin field in the near-zone limit of the Kerr black hole are identical to those of an AdS$_2$ black hole which enjoys the same basic properties of the Kerr black hole. Thanks to this identification, we calculate the spectrum of the quasinormal modes and the Love numbers of Kerr black holes using an AdS$_2$/CFT$_1$ correspondence and a group theoretical approach.
In this paper, we will analyze the thermodynamics of a small singly spinning Kerr-AdS black hole. As the black hole will be sufficient small, its temperature will be large and so we can not neglect the effects of thermal fluctuations. We will demonstrate that these thermal fluctuations correct the entropy of singly spinning Kerr-AdS black hole by a logarithmic correction term. We will analyze the implications of the logarithmic correction on other thermodynamic properties of this black hole, and analyze the stability of such a black hole. We will observe that this form of correction becomes im…
We investigate the conjectured bound on the Lyapunov exponent for a charged particle with angular motion in the Kerr-Newman-AdS black hole. The Lyapunov exponent is calculated based on the effective Lagrangian. We show that the negative cosmological constant reduces the chaotic behavior of the particle, namely, it decreases the Lyapunov exponent. Hence, the bound is more effective in the AdS spacetime than in the flat spacetime. Nevertheless, we find that the bound can be violated when the angular momenta of the black hole are turned on. Moreover, we show that in an extremal black hole, the bo…
We investigate quasinormal modes, greybody factor, and Hawking evaporation of a five-dimensional Kerr-anti de Sitter (AdS$_5$) black hole by solving a wave equation for a test massive scalar field in terms of the local Heun function. We clarify the distribution of the quasinormal modes satisfying the ingoing and decaying boundary conditions at the event horizon and conformal infinity, respectively, and their splitting behaviors in the complex frequency plane with respect to a variation of spin parameters. We also point out the existence of purely imaginary modes. Further, we develop a method t…
We establish an explicit correspondence of Einstein gravity on the squashed spheres that are the $U(1)$ bundles over $\mathbb{CP}^m$ to the Kaluza-Klein AdS gravity on the tori. This allows us to map the Ricci-flat Kerr metrics in odd dimensions with all equal angular momenta to charged Kaluza-Klein AdS black holes that can be lifted to become singly rotating M-branes and D3-branes. Furthermore, we find maps between Ricci-flat gravitational instantons to the AdS domain walls. In particular the supersymmetric bolt instantons correspond to domain walls that can be interpreted as distributed M-br…
We investigate the laws of thermodynamics and weak cosmic censorship conjecture in the normal and extended phase space of a Kerr-AdS black hole by analyzing the energy-momentum relation of the absorbed fermion dropping into the horizon. In the normal phase space, the first law, second law as well as the weak cosmic censorship conjecture are found to be valid in all the initial states of the black hole. However, in the extended phase space, although the first law and weak cosmic censorship conjecture are still valid, the second law becomes more subtle. We find that the validity or violation of …
Thermodynamics of Dual CFTs for Kerr-AdS Black Holes
最近Gibbons { \it et al.}在hep-th/0408217中定义了任意维中具有最大转动参数数的Kerr-AdS黑洞的一组守恒量。这组守恒量是相对于一个在无穷远处不旋转的坐标系定义的。另一方面，对于Kerr-AdS黑洞还有另一组守恒量，由Hawking { \it et al.}在HEP-TH/9811056中，其是相对于在无限远处旋转的框架测量的。Gibbons { \it等人}明确表明，由它们定义的量满足黑洞热力学第一定律，而霍金{ \it et al.}不要遵守第一条法则。本文通过将体热力学量映射到AdS空间的边界上，讨论了对偶CFTs对Kerr-AdS黑洞的热力学性质.我们发现，只有当对偶CFTs的热力学量是由Hawking { \it et al.}给出的体量集合导出时，这些热力学量才满足热力学第一定律和Cardy-Verlinde公式.我们讨论了我们的结果的含义。
We show that cosmic censorship takes an exceptionally complex and interesting form in the case of five-dimensional AdS-Kerr black holes, due to the unusually distant relation obtaining in that case between the black hole parameters and the physical mass and angular momentum. One finds that, in this case, censorship is less restrictive than one might hope: it apparently allows some rather bizarre behaviour, and in particular does not prohibit arbitrarily large angular momenta. We find however that most of the unwelcome geometries permitted by censorship can be eliminated by requiring stability …
The first law of black hole mechanics, which relates the change of energy to the change of entropy and other conserved charges, has been the main motivation for probing the thermodynamic properties of black holes. In this work, we investigate the thermodynamics of Kerr Taub-NUT AdS black holes. We present geometric Komar definitions for the black hole charges, that by construction satisfy the Smarr formula. Further, by a scaling argument based on Euler's theorem, we establish the first law for the Kerr Taub-NUT AdS black holes. The corresponding first law includes variations in the cosmologica…
As with any black hole, asymptotically anti-de Sitter Kerr black holes are described by a small number of parameters, including a "mass parameter" $M$ that reduces to the AdS-Schwarzschild mass in the limit of vanishing angular momentum. In sharp contrast to the asymptotically flat case, the horizon area of such a black hole increases with the angular momentum parameter $a$ if one fixes $M$, this appears to mean that the Penrose process in this case would violate the Second Law of black hole thermodynamics. We show that the correct procedure is to fix not $M$ but rather the "physical" mass $E=…
We search for a possible relation between weak gravity conjecture and conformal field theory in the hyperscaling violating and Kerr-Newman-AdS black holes. We deal with the critical points of the black hole systems through the correlation function introduced in conformal field theory. We discuss the weak gravity conjecture conditions by the imaginary part of the energy obtained from the critical points and their poles. Under the assumptions $z=1$, $d=1$ and $θ\rightarrow0^{-}$, we link weak gravity conjecture to the hyperscaling violating black holes due to the existence of $r_{H}$ larger and …
We analyze the Ansatz of separability for Maxwell equations in generically spinning, five-dimensional Kerr-AdS black holes. We find that the parameter μintroduced in a previous work by O. Lunin can be interpreted as apparent singularities of the resulting radial and angular equations. Using isomonodromy deformations, we describe a non-linear symmetry of the system, under which μis tied to the Painlevé VI transcendent. By translating the boundary conditions imposed on the solutions of the equations for quasinormal modes in terms of monodromy data, we find a procedure to fix μand study the behav…
