In this paper we investigate the thermodynamics of the inner horizon and its implication on the holographic description of the black hole. We focus on the black holes with two physical horizons. Under reasonable assumption, we prove that the first law of thermodynamics of the outer horizon always indicates that of the inner horizon. As a result, the fact that the area product being mass-independent is equivalent to the relation $T_+S_+=T_-S_-$, with $T_\pm$ and $S_\pm$ being the Hawking temperatures and the entropies of the outer and inner horizon respectively. We find that the mass-independence of area product breaks down in general Myers-Perry black holes with spacetime dimension $d\geq6$ and Kerr-AdS black holes with $d\geq4$.
Moreover we discuss the implication of the first laws of the outer and inner horizons on the thermodynamics of the right- and left-moving sectors of dual CFT in Kerr/CFT correspondence. We show that once the relation $T_+S_+=T_-S_-$ is satisfied, the central charges of two sectors must be same. Furthermore from the thermodynamics relations, we read the dimensionless temperatures of microscopic CFT, which are in exact agreement with the ones obtained from hidden conformal symmetry in the low frequency scattering off the black holes, and then determine the central charges. This method works well in well-known cases in Kerr/CFT correspondence, and reproduce successfully the holographic pictures for 4D Kerr-Newman and 5D Kerr black holes. We go on to predict the central charges and temperatures of a possible holographic CFT description dual to 5D doubly rotating black ring.
In this article, we review recent studies on multiple dual 2D CFT descriptions of the Kerr-Newman black hole, in terms of the Kerr/CFT and Reissner-Nordström/CFT correspondences. A microscopic hair conjecture is suggested.
We investigate the recently proposed Kerr/CFT correspondence in the context of rotating spacetimes with a NUT twist. The Kerr/CFT correspondence states that the near-horizon states of an extremal four (or higher) dimensional black hole could be identified with a certain chiral conformal field theory. The corresponding Virasoro algebra is generated with a class of diffeomorphism which preserves an appropriate boundary condition on the near-horizon geometry. We try to understand the analog of singularities in the context of dual chiral CFT. Explicitly, we use Kerr/CFT correspondence to show that…
We study real-time correlators in the Kerr/CFT correspondence. The near-horizon geometry of extreme and near-extremal Kerr black holes can be taken as warped spacetimes with the warping factors depending on the transverse radius and the angular variable. By considering the Kerr/CFT correspondence as a generalized warped AdS/CFT correspondence, we show how to compute the CFT real-time correlation functions. We find that the retarded Green's functions, the cross sections and the quasi-normal modes are all in perfect match with the predictions of the dual CFT. The same analysis is also generalize…
We give a short introduction, beginning with the Kerr geometry itself, to the basic results, motivation, open problems and future directions of the Kerr/CFT correspondence.
We extend the conjectured Kerr/CFT correspondence to the case of extremal Kerr black holes immersed by an magnetic field, namely the extremal Melvin-Kerr black holes. We compute the central charge which appears in the associated Virasoro algebra generated by a class of diffeomorphisms that satisfies a set of boundary conditions in the near horizon of an extremal Melvin-Kerr black hole. Our results support the Kerr/CFT conjecture, where the macroscopic Bekenstein-Hawking entropy for an extremal Melvin-Kerr black hole matches the result obtained from a dual 2D CFT microscopic computation using C…
In this paper, we use the appropriate boundary action for the vector fields near the horizon of near extremal Kerr black hole to calculate the two-point function for the vector fields in Kerr/CFT correspondence. We show the gauge-independent part of the two-point function is in agreement with what is expected from CFT.
In this paper, we study the real-time correlators in Kerr/CFT, in the low frequency limit of generic non-extremal Kerr(-Newman) black holes. From the low frequency scattering of Kerr-Newman black holes, we show that for the uncharged scalar scattering, there exists hidden conformal symmetry on the solution space. Similar to Kerr case, this suggests that the Kerr-Newman black hole is dual to a two-dimensional CFT with central charges $c_L=c_R=12J$ and temperatures $T_L=\frac{(r_++r_-)-Q^2/M}{4πa}, T_R=\frac{r_+-r_-}{4πa}$. Using the Minkowski prescription, we compute the real-time correlators o…
Similarly as in AdS/CFT, the requirement that the action for spinors be stationary for solutions to the Dirac equation with fixed boundary conditions determines the form of the boundary term that needs to be added to the standard Dirac action in Kerr/CFT. We determine this boundary term and make use of it to calculate the two-point function for spinor fields in Kerr/CFT. This two-point function agrees with the correlator of a two dimensional relativistic conformal field theory.
We study another realization of the Kerr/CFT correspondence. By imposing new asymptotic conditions for the near horizon geometry of Kerr black hole, an asymptotic symmetry which contains all of the exact isometries can be obtained. In particular, the Virasoro algebra can be realized as an enhancement of SL(2,R) symmetry of the AdS geometry. By using this asymptotic symmetry, we discuss finite temperature effects and show the correspondence concretely.
We apply a recently proposed Kerr/CFT correspondence to extremal supersymmetric five-dimensional charged spinning black holes, constructed by Breckenridge, Myers, Peet and Vafa. By computing the central charge of the dual CFT and Frolov-Thorne temperature, Cardy's formula succeeds in reproducing Bekenstein-Hawking area law.
Motivated by the Kerr-CFT conjecture, we investigate perturbations of the near-horizon extreme Kerr spacetime. The Teukolsky equation for a massless field of arbitrary spin is solved. Solutions fall into two classes: normal modes and traveling waves. Imposing suitable (outgoing) boundary conditions, we find that there are no unstable modes. The explicit form of metric perturbations is obtained using the Hertz potential formalism, and compared with the Kerr-CFT boundary conditions. The energy and angular momentum associated with scalar field and gravitational normal modes are calculated. The en…
We compute greybody factors for near extreme Kerr black holes in D=4 and D=5. In D=4 we include four charges so that our solutions can be continuously deformed to the BPS limit. In D=5 we include two independent angular momenta so Left-Right symmetry is incorporated. We discuss the CFT interpretation of our emission amplitudes, including the overall frequency dependence and the dependence on all black hole parameters. We find that all additional parameters can be incorporated Kerr/CFT, with central charge independent of U(1) charges.
It was proposed recently that the near-horizon states of an extremal four-dimensional Kerr black hole could be identified with a certain chiral conformal field theory whose Virasoro algebra arises as an asymptotic symmetry algebra of the near-horizon Kerr geometry. Supportive evidence for the proposed duality came from the equality of the microscopic entropy of the CFT, calculated by means of the Cardy formula, and the Bekenstein-Hawking entropy of the extremal Kerr black hole. In this paper we examine the proposed Kerr/CFT correspondence in a broader context. In particular, we show that the m…
It has been shown by A. Sen that logarithmic corrections to the black hole area-entropy law are entirely determined macroscopically from the massless particle spectrum. They therefore serve as powerful consistency checks on any proposed enumeration of quantum black hole microstates. Sen's results include a macroscopic computation of the logarithmic corrections for a five-dimensional near extremal Kerr-Newman black hole. Here we compute these corrections microscopically using a stringy embedding of the Kerr/CFT correspondence and find perfect agreement.
There are two known CFT duals, namely the J-picture and the Q-picture, for a four-dimensional Kerr-Newman black hole, corresponding to the angular momentum $J$ and the electric charge $Q$ respectively. In our recent study we found a one-parameter class of CFT duals for extremal Kerr-Newman black hole, connecting these two pictures. In this paper we study these novel CFT duals for the generic non-extremal Kerr-Newman black hole. We investigate the hidden conformal symmetry in the low frequency scattering off Kerr-Newman black hole, from which the dual temperatures could be read. We find that th…
We demonstrate that Kerr-CFT duality can be extended to super-entropic black holes, which have non-compact horizons with finite area. We demonstrate that this duality is robust insofar as the ultra-spinning limit of a Kerr-AdS black hole (which yields the super-entropic class)commutes with the near-horizon limit (which yields the Kerr-CFT duality). Consequently the Bekeinstein-Hawking and the CFT entropies are equivalent. We show that the duality holds for both singly-spinning super-entropic black holes in 4 dimensions and for doubly-spinning super-entropic black holes of gauged supergravity i…
We extend the method of Kerr/CFT correspondence recently proposed in arXiv:0809.4266 [hep-th] to the extremal (charged) Kerr black hole embedded in the five-dimensional Gödel universe. With the aid of the central charges in the Virasoro algebra and the Frolov-Thorne temperatures, together with the use of the Cardy formula, we have obtained the microscopic entropies that precisely agree with the ones macroscopically calculated by Bekenstein-Hawking area law.
We point out that the entropies of black holes in general diffeomorphism invariant theories, computed using the Kerr-CFT correspondence and the Wald formula (as implemented in the entropy function formalism), need not always agree. A simple way to illustrate this is to consider Einstein-Gauss-Bonnet gravity in four dimensions, where the Gauss-Bonnet term is topological. This means that the central charge of Kerr-CFT computed in the Barnich-Brandt-Compere formalism remains the same as in Einstein gravity, while the entropy computed using the entropy function gives a universal correction proport…
We construct a family of vector fields that generate local symmetries in the solution space of low frequency massless field perturbations in the general Kerr geometry. This yields a one-parameter family of SL(2,R)x SL(2,R) algebras. We identify limits in which the SL(2,R)xSL(2,R) algebra contracts to an SL(2,R) symmetry of the Schwarzschild background. We note that for a particular value of our new free parameter, the symmetry algebra generates the quasinormal mode spectrum of a Kerr black hole in the large damping limit, suggesting a connection between the hidden conformal symmetry and a fund…
The correspondence between the Kerr black hole and a boundary CFT has been conjectured recently. The conjecture has been proposed first only for the half of the CFT, namely for left movers. For right movers, the correspondence has been also found out through the suitable asymptotic boundary condition. However, the boundary conditions for these two studies are exclusive to each other. The boundary condition for left movers does not allow the symmetry of right movers, and vice versa. We propose new boundary condition which allows both of left and right movers.
We investigate linear perturbations of spin-s fields in the Kerr-AdS black hole and in its near-horizon geometry (NHEK-AdS), using the Teukolsky master equation and the Hertz potential. In the NHEK-AdS geometry we solve the associated angular equation numerically and the radial equation exactly. Having these explicit solutions at hand, we search for linear mode instabilities. We do not find any (non-)axisymmetric instabilities with outgoing boundary conditions. This is in agreement with a recent conjecture relating the linearized stability properties of the full geometry with those of its near…
The near-horizon geometry of the extremal four-dimensional Kerr black hole and certain generalizations thereof has an SL(2,R) x U(1) isometry group. Excitations around this geometry can be controlled by imposing appropriate boundary conditions. For certain boundary conditions, the U(1) isometry is enhanced to a Virasoro algebra. Here, we propose a free-field construction of this Virasoro algebra.
We compute the boundary stress-energies of time-dependent asymptotically AdS spacetimes in 5 and 7 dimensions, and find that their traces are equal to the respective 4 and 6 dimensional field-theoretic trace anomalies. This provides good supporting evidence in favour of the AdS/CFT correspondence in time-dependent backgrounds.
We show that the near horizon regime of a Kerr-Newman-$AdS$ (KN$AdS$) black hole, given by its two dimensional analogue $a la$ Robinson and Wilczek (2005 Phys. Rev. Lett. 95 011303), is asymptotically $AdS_2$ and dual to a one dimensional quantum conformal field theory (CFT). The s-wave contribution of the resulting CFT's energy-momentum-tensor together with the asymptotic symmetries, generate a centrally extended Virasoro algebra, whose central charge reproduces the Bekenstein-Hawking entropy via Cardy's Formula. Our derived central charge also agrees with the near extremal Kerr/CFT Correspon…
In this short note we extend the work of 1401.3746 about gravity waves by a massive orbiting star in an extremal Kerr black hole to an extremal Kerr- Newman black hole for scalar radiation, and still find that it has a CFT interpretation from Kerr-Newman/CFT. In addition, we investigate on electromagnetic radiation with Kerr/CFT, which a detailed analysis isn't given by 1401.3746.
We find the explicit form of two-point function for the conformal spin-2 energy momentum operators on the near horizon of a near extremal Kerr black hole by variation of a proper boundary action. In this regard, we consider an appropriate boundary action for the gravitational perturbation of the Kerr black hole. We show that the variation of the boundary action with respect to the boundary fields yields the two-point function for the energy momentum tensor of a conformal field theory. We find agreement between the two-point function and the correlators of the dual conformal field theory to the…
Ingoing and outgoing principal null geodesics in Kerr spacetimes are characterized as part of parametrized families of strings in complex Kerr geometry and are associated with holomorphic curves in twistor space with help of the Kerr theorem. They are defined on 2-dimensional twistor manifolds, one for outgoing and one for ingoing principal null congruences, and are solutions of free twistor string models on these 2-dimensional twistor manifolds. Such a twistor string model implies a conformal field theory and, assuming the applicability of the Cardy formula, agreement with the Bekenstein-Hawk…
A new holographic duality named Kerr/CFT correspondence was recently proposed to derive the statistical entropy of four-dimensional extremal Kerr black holes via identifying the quantum states in the near-horizon region with those of two-dimensional conformal field theory living on the boundary. In this paper, we apply this method to investigate five-dimensional extremal Kerr and Cvetič-Youm black holes with squashed horizons in different coordinates and find that the near-horizon geometries are not affected by the squashing transformation. Our investigation shows that the microscopic entropie…
In this paper, we suggest that there are two different individual 2D CFTs holographically dual to the Kerr-Newman black hole, coming from the corresponding two possible limits --- the Kerr/CFT and Reissner-Nordström/CFT correspondences, namely there exist the Kerr-Newman/CFTs dualities. A probe scalar field at low frequencies turns out can exhibit two different 2D conformal symmetries (named by $J$- and $Q$-pictures, respectively) in its equation of motion when the associated parameters are suitably specified. These twofold dualities are supported by the matchings of entropies, absorption cros…
The near-horizon geometries of the extremal Kerr black hole and certain generalizations thereof are considered. Their isometry groups are all given by SL(2,R) x U(1). The usual boundary conditions of the Kerr/CFT correspondence enhance the U(1) isometry to a Virasoro algebra. Various alternatives to these boundary conditions are explored. Partial classifications are provided of the boundary conditions enhancing the SL(2,R) isometries or separately the U(1) isometry to a Virasoro algebra. In the case of SL(2,R)-enhancing boundary conditions of a near-horizon geometry of the type considered, the…
We study solutions of type IIB supergravity which are SL(2,R) x SU(2) x U(1)^2 invariant deformations of AdS_3 x S^3 x K3 and take the form of products of self-dual spacelike warped AdS_3 and a deformed three-sphere. One of these backgrounds has been recently argued to be relevant for a derivation of Kerr/CFT from string theory, whereas the remaining ones are holographic duals of two-dimensional dipole theories and their S-duals. We show that each of these backgrounds is holographically dual to a deformation of the DLCQ of the D1-D5 CFT by a specific supersymmetric (1,2) operator, which we wri…
Following Kerr/CFT correspondence, we compute the entropy of five-dimensional supersymmetric rotating BMPV black holes.We successfully reproduce Iyer-Wald formula in the presence of Gauss-Bonnet terms from the viewpoint of microscopic CFT. This further supports the higher-derivative version of Kerr/CFT prescription proposed in arXiv:0903.4176 for four-dimensional extremal Kerr black holes.
We consider the Kerr-de Sitter (Kerr-dS) black hole in various dimensions. Introducing a counterterm, we show that the total action of these spacetimes are finite. We compute the masses and the angular momenta of Kerr-dS spaces with one rotational parameter in four, five and seven dimensions. These conserved charges are also computed for the case of Kerr-dS space with two rotational parameters in five dimensions. Although the angular momentum density due to the counterterm is nonzero, it gives a vanishing contribution to the total angular momentum. We also find that the total angular momentum …
We extend the recently proposed Kerr/CFT correspondence to examine the dual conformal field theory of Kaluza-Klein black hole. For the extremal Kaluza-Klein black hole, the central charge and temperature of the dual conformal field are calculated, and the microscopic entropy calculated by using Cardy formula agrees with the Bekenstein-Hawking entropy of extremal Kaluza-Klein black hole. For the non-extremal case, we investigate the hidden conformal symmetry of Kaluza-Klein black hole by studying the near-region wave equation of a neutral massless scalar field, and find the left and right tempe…
Massless fields propagating in a generic Kerr black hole background enjoy a hidden SL(2,R)xSL(2,R) symmetry. We determine how the exact mode functions decompose into representations of this symmetry group. This extends earlier results on the low frequency limit of the massless scalar case to finite frequencies and general spin. As an application, we numerically determine the parameters of the representations that appear in quasinormal modes. These results represent a first step to formulating a more precise mapping to a holographic dual conformal field theory for generic black holes.
The Kerr/CFT correspondence employs the Cardy formula to compute the entropy of the left moving CFT states. This computation, which correctly reproduces the Bekenstein--Hawking entropy of the four-dimensional extremal Kerr black hole, is performed in a regime where the temperature is of order unity rather than in a high-temperature regime. We show that the comparison of the entropy of the extreme Kerr black hole and the entropy in the CFT can be understood within the Cardy regime by considering a D0-D6 system with the same entropic properties.
We study the conformal symmetry described by $SL(2,R)_L \times SL(2,R)_R$ in the nonextremal Kerr black hole case. We calculate the central charges $c_{L,R}$ separately on a stretched horizon by the Hamiltonian gravity. In order to get two sets of conformal symmetry, we consider two Killing vectors each of which depends on either one of the two independent coordinates separated in the spirit of point-splitting from the angular coordinate of the corotating frame at the horizon. Then, we obtain the Bekenstein-Hawking entropy by the Cardy formula.
We investigate the recently proposed Kerr/CFT correspondence in the context of heterotic string theory. The Kerr/CFT correspondence states that the near-horizon states of an extremal four (or higher) dimensional black hole could be identified with a certain chiral conformal field theory under the conjecture that the central charges from the non-gravitational fields vanish. The corresponding Virasoro algebra is generated by a class of diffeomorphisms which preserves the appropriate boundary conditions on the near-horizon geometry. To understand the chiral conformal field theory, we consider the…
We demonstrate that rotating dyonic black holes in Einstein-Maxwell-Dilaton-Axion (EMDA) theory is holographically dual with 2D conformal field theory. We first investigate the duality on dyonic Kerr-Sen black hole with non-vanishing dilaton and axion charges. The near-horizon geometry of extremal dyonic Kerr-Sen spacetime possesses the $SL(2,R) \times U (1)$ isometry allowing to employ the asymptotic symmetry group method to find the corresponding central charge. We find two different branches of the mass which correspond to CFT with two different central charges $c_L=12am_+$ and $c_L=12am_-$…
We consider the quasilocal thermodynamics of rotating black holes in asymptotic de Sitter spacetimes. Using the minimal number of intrinsic boundary counterterms, we carry out an analysis of the quasilocal thermodynamics of Kerr-de Sitter black holes for virtually all possible values of the mass, rotation parameter and cosmological constant that leave the quasilocal boundary inside the cosmological event horizon. Specifically, we compute the quasilocal energy, the conserved charges, the temperature and the heat capacity for the $(3+1)$-dimensional Kerr-dS black holes. We perform a quasilocal s…
We compute three-point correlation functions in the near-extremal, near-horizon region of a Kerr black hole, and compare to the corresponding finite-temperature conformal field theory correlators. For simplicity, we focus on scalar fields dual to operators ${\cal O}_h$ whose conformal dimensions obey $h_3=h_1+h_2$, which we name \emph{extremal} in analogy with the classic $AdS_5 \times S^5$ three-point function in the literature. For such extremal correlators we find perfect agreement with the conformal field theory side, provided that the coupling of the cubic interaction contains a vanishing…
In this paper, we study the CFT duals for extreme black holes in the stretched horizon formalism. We consider the extremal RN, Kerr-Newman-AdS-dS, as well as the higher dimensional Kerr-AdS-dS black holes. In all these cases, we reproduce the well-established CFT duals. Actually we show that for stationary extreme black holes, the stretched horizon formalism always gives rise to the same dual CFT pictures as the ones suggested by ASG of corresponding near horizon geometries. Furthermore, we propose new CFT duals for 4D Kerr-Newman-AdS-dS and higher dimensional Kerr-AdS-dS black holes. We find …
The Kerr/CFT correspondence is a holographic duality between a two dimensional chiral conformal field theory (CFT) and the very near horizon limit of an extremal black hole, which includes an AdS2 structure. To understand the dual chiral CFT2, we apply the Kerr/CFT correspondence to a certain class of black holes embedded in string theory, which include the D1-D5-P and the BMPV black holes, and obtain the correct entropies for the black holes microscopically. These have an AdS3 structure in the near horizon geometry and an AdS2 structure in the very near horizon geometry. We identified one of …
It has been proposed that a hidden conformal field theory (CFT) governs the dynamics of low frequency scattering in a general Kerr black hole background. We further investigate this correspondence by mapping higher order corrections to the massless wave equations in a Kerr background to an expansion within the CFT in terms of higher dimension operators. This implies the presence of infinite towers of CFT primary operators with positive conformal dimensions compatible with unitarity. The exact Kerr background softly breaks the conformal symmetry and the scaling dimensions of these operators run…
Holographic Renormalization Group (RG) in nine dimensions is considered. The d8 holographic conformal anomaly is found. It should correspond to d8 CFT in AdS_9/CFT_8 correspondence. The comparison of holographic and QFT anomalies in d8 de Sitter space is done. It may give the indication for rigorous AdS_9/CFT_8 correspondence proposal.
We study real-time correlators in the warped AdS/CFT correspondence. We apply the prescription used in the usual AdS/CFT correspondence and obtain the retarded Green's functions for the scalar and vector fields in the spacelike warped and the null warped black hole backgrounds. We find that the retarded Green's functions and the cross sections are well consistent with the predictions from dual CFT. Our results not only support strongly the conjectured warped AdS/CFT correspondence, but also show that the usual relativistic AdS/CFT prescription of obtaining the real-time correlators remain effe…
In frames of dS/CFT correspondence suggested by Strominger we calculate holographic conformal anomaly for dual euclidean CFT. The holographic renormalization group method is used for this purpose. It is explicitly demonstrated that two-dimensional and four-dimensional conformal anomalies (or corresponding central charges) have the same form as those obtained in AdS/CFT duality.
We discuss dilatonic gravity (bulk theory) from the point of view of (generalized) AdS/CFT correspondence. Self-consistent dilatonic background is considered. It may be understood as two boundaries space where AdS boundary appears as infinite boundary and new (singular) boundary occurs at short distances. The two-point correlation function and conformal dimension for minimal and dilaton coupled scalar are found. Even for minimal scalar, the conformal dimension is found to be different on above two boundaries. Hence, new CFT appears in AdS/CFT correspondence at short distances. AdS/CFT correspo…
The prescription of the AdS/CFT correspondence is refined by using a regularization procedure, which makes is possible to calculate the divergent local terms in the CFT two-point function. We present the procedure for the example of the scalar field.
We expand on Klebanov and Witten's recent proposal for formulating the AdS/CFT correspondence using irregular boundary conditions. The proposal is shown to be correct to any order in perturbation theory.
We show some implications of the approach to AdS/CFT correspondence based on Type IIB string in the flat space-time with D3-branes proposed in our previous paper. We discuss a correspondence for high energy scattering amplitudes of N=4 super-Yang-Mills proposed recently. We also discuss AdS/CFT correspondence at finite temperature. Our approach provides clear understanding of these issues.
By taking the interacting spinor-scalar theory on the $AdS_{d+1}$ space we calculate the boundary CFT correlation functions using AdS/CFT correspondence.
We show that the spinning magnetic one-brane in minimal five-dimensional supergravity admits a decoupling limit that interpolates smoothly between a self-dual null orbifold of AdS_3 \times S^2 and the near-horizon limit of the extremal Kerr black hole times a circle. We use this interpolating solution to understand the field theory dual to spinning M5 branes as a deformation of the Discrete Light Cone Quantized (DLCQ) Maldacena-Stominger-Witten (MSW) CFT. In particular, the conformal weights of the operators dual to the deformation around AdS_3 \times S^2 are calculated. We present pieces of e…
We calculate the scalar quasinormal modes of warped $AdS_3$ black holes analytically. We find that in general they are not in agreement with the prediction of the usual AdS/CFT correspondence. Nevertheless, for the black hole not deviating far from BTZ black hole, the quasinormal frequencies are still well consistent with AdS/CFT correspondence.
