Jin-Ho Cho, Yumi Ko, Soonkeon Nam
Based on the entropy function formalism, we consider the extremal Kerr-(anti-)de Sitter black holes in 4-dimensions. Solving differential equations exactly, which are obtained by extremizing the entropy function, we find agreement of the result with Bekenstein-Hawking entropy. Concerning the higher derivative corrections, we extend the computation to the case with Gauss-Bonnet term.
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We show that extremal Kerr-Bolt spacetimes have a hidden conformal symmetry. In this regard, we consider the wave equation of a massless scalar field propagating in extremal Kerr-Bolt spacetimes and find in the "near region", the wave equation in extremal limit can be written in terms of the $SL(2,R)$ quadratic Casimir. Moreover, we obtain the microscopic entropy of the extremal Kerr-Bolt spacetimes also we calculate the correlation function of a near-region scalar field and find perfect agreement with the dual 2D CFT.
A quantum deformation of three-dimensional de Sitter space was proposed in hep-th/0407188. We use this to calculate the entropy of Kerr-de Sitter space, using a canonical ensemble, and find agreement with the semiclassical result.
The equation of cosmic string loops in Kerr-de Sitter spacetimes is derived. Having solved the equation numerically, we find that the loops can expand and exist except for too small ones.
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.
It is shown that the Dirac equations in general higher dimensional Kerr-NUT-de Sitter spacetimes are separated into ordinary differential equations.
We study spacetimes with a closed conformal Killing-Yano tensor. It is shown that the D-dimensional Kerr-NUT-de Sitter spacetime constructed by Chen-Lu-Pope is the only spacetime admitting a rank-2 closed conformal Killing-Yano tensor with a certain symmetry.
Generalized Kerr-NUT-de Sitter spacetime is the most general spacetime which admits a rank-2 closed conformal Killing-Yano tensor. It contains the higher-dimensional Kerr-de Sitter black holes with partially equal angular momenta. We study the separability of gravitational perturbations in the generalized Kerr-NUT-de Sitter spacetime. We show that a certain type of tensor perturbations admits the separation of variables. The linearized perturbation equations for the Einstein condition are transformed into the ordinary differential equations of Fuchs type.
We analyze the asymptotic symmetries of near extremal Kerr black holes in four dimensions using the AdS_2/CFT_1 correspondence. We find a Virasoro algebra with central charge c_R=12J that is independent from the Virasoro algebra (with the same central charge) that acts on the degenerate ground state. The energy of the excitations is computed as well, and we can use Cardy's formula to determine the near extremal entropy. Our result is consistent with the Bekenstein-Hawking area law for near extremal Kerr black holes.
We study the dynamical behavior of the dilaton in the background of three-dimensional Kerr-de Sitter space which is inspired from the low-energy string effective action. The Kerr-de Sitter space describes the gravitational background of a point particle whose mass and spin are given by $1-M$ and $J$ and its curvature radius is given by $\ell$. In order to study the propagation of metric, dilaton, and Kalb-Ramond two-form, we perform the perturbation analysis in the southern diamond of Kerr-de Sitter space including a conical singularity. It reveals a mixing between the dilaton and other unphys…
We explicitly calculate the Riemannian curvature of D-dimensional metrics recently discussed by Chen, Lu and Pope. We find that they can be concisely written by using a single function. The Einstein condition which corresponds to the Kerr-NUT-de Sitter metric is clarified for all dimensions. It is shown that the metrics are of type D.
Logarithmic Corrections for Near-extremal Kerr-Newman Black Holes
本文用欧几里得路径积分和改进的热核方法，计算了$\mathcal{N}=2$超引力中近极端Kerr-Newman黑洞熵的对数修正，控制了红外发散，结果可为微观理论检验。
Using the quasi-normal modes frequency of near extremal Schwarzschild-de Sitter black holes, we obtain area and entropy spectrum for black hole horizon. By using Boher-Sommerfeld quantization for an adiabatic invariant $I=\int {dE\over ω(E)}$, which $E$ is the energy of system and $ω(E)$ is vibrational frequency, we leads to an equally spaced mass spectrum. In the other term we extend directly the Kunstatter's approach [7] to determine mass and entropy spectrum of near extremal Schwarzschild-de Sitter black holes which is asymptotically de Sitter rather than asymptotically flat.
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.
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…
We construct a general class of non-extremal charged Kerr-de Sitter black holes in five dimensions, in which the two rotation parameters are set equal. There are three non-trivial parameters, namely the mass, charge and angular momentum. All previously-known cases, supersymmetric and non-supersymmetric, that have equal angular momenta are encompassed as special cases.
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 study extremal surfaces in the Schwarzschild de Sitter spacetime with real mass parameter. We find codim-2 timelike extremal surfaces stretching between the future and past boundaries that pass through the vicinity of the cosmological horizon in a certain limit. These are analogous to the surfaces in arXiv:1711.01107 [hep-th]. We also find spacelike surfaces that never reach the future/past boundaries but stretch indefinitely through the extended Penrose diagram, passing through the vicinity of the cosmological and Schwarzschild horizons in a certain limit. Further, these exhibit interestin…
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 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…
We study the near horizon 2d gravity theory which captures the near extremal thermodynamics of Kerr black holes where a linear combination of excess angular momentum $δJ $ and excess mass $δM$ is held fixed. These correspond to processes where both the mass and the angular momenta of extremal Kerr black holes are perturbed leaving them near extremal. For the Kerr $AdS_4$ we hold $δJ-\mathcal{L}\,δM=0 $ while for Myers-Perry(MP) type Kerr black hole in $AdS_5$ we hold $δJ_{φ_{1,2}}\hspace{-0.2cm}-\mathcal{L}_{φ_{1,2}}\,δM=0$. We show that in near horizon, the 2d Jackiw-Teitelboim theory is able…
I consider the (2+1)-dimensional Kerr-De Sitter space and its statistical entropy computation. It is shown that this space has only one (cosmological) event horizon and there is a phase transition between the stable horizon and the evaporating horizon at a point $M^2={1/3}J^2/l^2$ together with a lower bound of the horizon temperature. Then, I compute the statistical entropy of the space by using a recently developed formulation of Chern-Simons theory with boundaries, and extended Cardy's formula. This is in agreement with the thermodynamics formula.
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…
In this paper we show that the entropy of cosmological horizon in 4-dimensional Topological Kerr-Newman-de Sitter spaces can be described by the Cardy-Verlinde formula, which is supposed to be an entropy formula of conformal field theory in any dimension. Furthermore, we find that the entropy of black hole horizon can also be rewritten in terms of the Cardy-Verlinde formula for these black holes in de Sitter spaces, if we use the definition due to Abbott and Deser for conserved charges in asymptotically de Sitter spaces. Such result presume a well-defined dS/CFT correspondence, which has not y…
The thermodynamics and weak cosmic censorship conjecture in Reissner-Nordstr$\ddot{o}$m anti-de Sitter black holes are investigated by the scattering of the scalar field. The first law of thermodynamics in the non-extremal Reissner-Nordstr$\ddot{o}$m anti-de Sitter black hole is recovered by the scattering. The increase of the horizon radius indicates that the singularity is not naked in this black hole. For the near-extremal and extremal black holes, the validity is tested by the minimum values of the function $f$ at their final states. It is found that both of the near-extremal and extremal …
Further remarks on de Sitter space, extremal surfaces and time entanglement
本文进一步研究德西特空间中极值曲面与时间纠缠，通过解析延拓建立几何图像，提出伪熵解释，并探讨多子区域熵关系及未来-过去纠缠态。
Extremal scalar three-point correlators in the near-NHEK geometry of Kerr black holes have recently been shown to agree with the result expected from a holographically dual non-chiral two-dimensional conformal field theory. In this paper we extend this calculation to extremal three-point functions of scalars in a general Kerr black hole which need not obey the extremality condition $M=\sqrt{J}$. It was recently argued that for low frequency scalars in the Kerr geometry there is a dual conformal field theory description which determines the interactions in this regime. Our results support this …
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…
We prove that the only four dimensional, stationary, rotating, asymptotically flat (analytic) vacuum black hole with a single degenerate horizon is given by the extremal Kerr solution. We also prove a similar uniqueness theorem for the extremal Kerr-Newman solution. This closes a longstanding gap in the black hole uniqueness theorems.
We study the family of Einstein-Maxwell instantons associated with the Kerr-Newman metrics with a positive cosmological constant. This leads to a quantisation condition on the masses and charges of the resulting Euclidean solutions.
We find an exact solution of Kerr-Newman-de Sitter type on the braneworld(4D) of the DGP model. When a constant 4D Ricci scalar is assumed, only zero(flat) and a positive(de-Sitter) values satisfy the Hamiltonian constraint equation coming from the extra dimension. With a Z_2-symmetry across the brane and a stationary and axisymmetric metric ansatz on the brane, we solve the constraint equation exactly in the Kerr-Schild form with de-Sitter background. In the de-Sitter background this Kerr-Schild solution is well behaved under Boyer-Lindquist transformation: the constraint equation is preserve…
Generalising arXiv:1511.08496, we construct further families of compact Einstein-Maxwell instantons associated with the Kerr-Newman metrics with a positive cosmological constant.
We investigate linear, spin-field perturbations of Kerr black holes in the extremal limit throughout the complex-frequency domain. We calculate quasi-normal modes of extremal Kerr, as well as of near-extremal Kerr, via a novel approach: using the method of Mano, Suzuki and Takasugi (MST). We also show how, in the extremal limit, a branch cut is formed at the superradiant-bound frequency, $ω_{SR}$, via a simultaneous accumulation of quasi-normal modes and totally-reflected modes. For real frequencies, we calculate the superradiant amplification factor, which yields the amount of rotational ener…
We use Heun type solutions given in \cite{Suzuki} for the radial Teukolsky equation, written in the background metric of the Kerr-Newman-de Sitter geometry, to calculate the quasinormal frequencies for polynomial solutions and the reflection coefficient for waves coming from the de Sitter horizon and reflected at the outer horizon of the black hole.
The higher-dimensional Kerr-NUT-de Sitter spacetime describes the general rotating asymptotically de Sitter black hole with NUT parameters. It is known that such a spacetime possesses a rank-2 closed conformal Killing-Yano (CKY) tensor as a ``hidden'' symmetry which provides the separation of variables for the geodesic equations and Klein-Gordon equations. We present a classification of higher-dimensional spacetimes admitting a rank-2 closed CKY tensor. This provides a generalization of the Kerr-NUT-de Sitter spacetime. In particular, we show that the Kerr-NUT-de Sitter spacetime is the only s…
Although the circular photon orbit and ISCO for the Kerr black hole remain distinct from each other and from the horizon in the extremal spin limit on a constant Boyer-Lindquist time slice, on a horizon-crossing slice they both coincide with the null generators of the horizon.
It is believed that extremal black holes do not emit Hawking radiation as understood by taking extremal limits of non-extremal black holes. However, it is debated whether one can make such conclusion reliably starting from an extremal black hole, as the associated Bogoliubov coefficients which relate ingoing and outgoing field modes do not satisfy the required consistency condition. We address this issue in a canonical approach firstly by presenting an exact canonical derivation of the Hawking effect for non-extremal Kerr black holes. Subsequently, for extremal Kerr black holes we show that th…
We compute the second Seely-DeWitt coefficient of the kinetic operator of the metric and gauge fields in Einstein-Maxwell theory in an arbitrary background field configuration. We then use this result to compute the logarithmic correction to the entropy of an extremal Kerr-Newmann black hole.
We show how to compute the mass of a Kerr-anti-de Sitter spacetime with respect to the anti-de Sitter background in any dimension, using a superpotential which has been derived from standard Noether identities. The calculation takes no account of the source of the curvature and confirms results obtained for black holes via the first law of thermodynamics.
Unlike the extremal Reissner - Nordström black hole in ordinary spacetime, the one in anti-de Sitter spacetime is a minimum of action and has zero entropy if quantization is carried out after extremalization. However, if extremalization is carried out after quantization, then the entropy is a quarter of the area as in the usual case.
It has been shown that extremal Kerr black holes can be used as particle accelerators and arbitrarily high energy may be obtained near the event horizon. We study particle collisions near the event horizon (outer horizon) and Cauchy horizon (inner horizon) of a non-extremal Kerr black hole. Firstly, we provide a general proof showing that particles cannot collide with arbitrarily high energies at the outter horizon. Secondly, we show that ultraenergetic collisions can occur near the inner horizon of a Kerr black hole with any spin parameter $a$.
We first calculate equations of motion for particles in the Kerr-Sen-de Sitter black hole spacetime. Then in the eikonal regime, we analytically obtain the quasi-normal resonant modes of massless neutral scalar field perturbation and find its imaginary part to be characterized by the surface gravity of the near-extremal Kerr-Sen-de Sitter black hole with Cauchy horizon approaching the event horizon. We further show that the Penrose strong cosmic censorship conjecture is thus respected in this spacetime with dilaton scalar field and axion pseudoscalar field.
In the context of the Hamiltonian formulation of the teleparallel equivalent of general relativity we compute the gravitational energy of Kerr and Kerr Anti-de Sitter (Kerr-AdS) space-times. The present calculation is carried out by means of an expression for the energy of the gravitational field that naturally arises from the integral form of the constraint equations of the formalism. In each case, the energy is exactly computed for finite and arbitrary spacelike two-spheres, without any restriction on the metric parameters. In particular, we evaluate the energy at the outer event horizon of …
We use zero angular momentum null geodesics in the Kerr-de Sitter spacetime to transform the metric in a generalised Bondi coordinate system. We write the metric components explicitly. Next, we choose the radial coordinate to be the areal coordinate and write the asymptotic metric in the Bondi-Sachs gauge.
Love Numbers for Extremal Kerr Black Hole
本文研究了极端零温度克尔黑洞的引力潮汐洛夫数，证明其有限且具有耗散性质，并利用Leaver-MST方法给出了低频下的显式表达式。
We consider Kerr-de Sitter spacetimes and evaluate their mass, angular momentum and entropy according to the boundary counterterm prescription. We provide a physicall interpretation for angular velocity and angular momentum at future/past infinity. We show that the entropy of the four-dimensional Kerr-de Sitter spacetimes is less than of pure de Sitter spacetime in agreement to the entropic N-bound. Moreover, we show that maximal mass conjecture which states any asymptotically de Sitter spacetime with mass greater than de Sitter has a cosmological singularity is respected by asymptotically de …
We compute the mass and angular momenta of rotating anti-de Sitter spacetimes in Einstein-Gauss-Bonnet theory of gravity using a superpotential derived from standard Noether identities. The calculation relies on the fact that the Einstein and Einstein-Gauss-Bonnet vacuum equations are the same when linearized on maximally symmetric backgrounds and uses the recently discovered D-dimensional Kerr-anti-de Sitter solutions to Einstein's equations.
We describe three-dimensional Kerr-de Sitter space using similar methods as recently applied to the BTZ black hole. A rigorous form of the classical connection between gravity in three dimensions and two-dimensional conformal field theory is employed, where the fundamental degrees of freedom are described in terms of two dependent SL(2,C) currents. In contrast to the BTZ case, however, quantization does not give the Bekenstein-Hawking entropy connected to the cosmological horizon of Kerr-de Sitter space.
Strong Cosmic Censorship in Kerr-Newman-de Sitter
本文通过扫描 Kerr-Newman-de Sitter 黑洞参数空间并分析线性标量场扰动与准正常模谱，确定了 SCC 由遵从转为违反的大致球形壳层边界。
Recently, Banãdos, Silk and West (BSW) found that the center-of-mass energy of two colliding test particles in the neighborhood of an extreme Kerr black hole could be arbitrarily high when one particle has the critical angular momentum $L_\text{C}$. In their paper, they considered the black holes living in a Minkowski space-time with a zero cosmological constant. In this work, we study this process of particles in the backgrounds of the Kerr black holes living in a space-time with a nonzero cosmological constant. We find that for kerr black holes living in a space-time with a negative cosmolog…
The quantum tunneling radiation of fermions with arbitrary spin at the event horizon of Kerr-de Sitter black hole is accurately modified by using the dispersion relation proposed in the study of string theory and quantum gravitational theory. The derived tunneling rate and temperature at the black hole horizons are analyzed and studied.
We investigate in detail the mechanism of superradiance to render the instability of Kerr-de Sitter black holes in scalar-tensor gravity. Our results provide more clues to examine the scalar-tensor gravity in the astrophysical black holes in the universe with cosmological constant. We also discuss the spontaneous scalarization in the de Sitter background and find that this instability can also happen in the spherical de Sitter configuration in a special style.
We study the superradiance instability of charged massive scalar field in the background of Kerr-Newman-anti-de Sitter black hole. By employing the asymptotic matching technique to solve Klein-Gordon equation analytically, the complex parts of quasinormal frequencies are shown to be positive in the regime of superradiance. Because the calculation is performed in the approximation of small black hole, the result indicates that small Kerr-Newman-anti-de Sitter black hole is unstable against the massive scalar field perturbation with small charge.
Different forms of the metric for the Kerr-NUT-(anti-)de Sitter space-time are being widely used in its extension to higher dimensions. The purpose of this note is to relate the parameters that are being used to the physical parameters (mass, rotation, NUT and cosmological constant) in the basic four dimensional situation.
Superradiance in black hole spacetimes can trigger instabilities. Here we show that, due to superradiance, small Kerr-anti-de Sitter black holes are unstable. Our demonstration uses a matching procedure, in a long wavelength approximation.
We show that the horizon instability of the extremal Kerr black hole is associated with a singular branch point in the Green function at the superradiant bound frequency. We study generic initial data supported away from the horizon and find an enhanced growth rate due to nonaxisymmetric modes. The growth is controlled by the conformal weight of each mode. We speculate on connections to near-extremal black holes and holographic duality.
We analyze the near horizon symmetry of the extremal Kerr black hole within the framework of Poincaré gauge theory (PG) for two important limiting cases: Riemannian and teleparallel solution. We show that the algebra of canonical generators is realized by Virasoro algebra, with central charge which depends on the black hole horizon radius . The conformal entropy of the black hole is obtained via Cardy formula.
As in the grand canonical treatment of Reissner - Nordström black holes in anti-de Sitter spacetime, the canonical ensemble formulation also shows that non-extremal black holes tend to have lower action than extremal ones. However, some small non-extremal black holes have higher action, leading to the possibility of transitions between non-extremal and extremal black holes.
It has been recently shown that magnetic reconnection can provide us a novel mechanism to extract black hole rotational energy from a Kerr black holes. In this paper, we study the energy extraction from the Kerr-de Sitter black hole via this magnetic reconnection process. The result shows that, with the increase of the cosmological constant, a slowly spinning Kerr-de Sitter black hole can implement the energy extraction better than its Kerr counterpart. Interestingly, although the numerical results show that the maximum values of the power and efficiency slightly decrease with the cosmological…
We study Killing horizons and their neighbourhoods in the Kerr-NUT-(anti-)de Sitter and the accelerated Kerr-NUT-(anti-)de Sitter spacetimes. The geometries of the horizons have an irremovable singularity at one of the poles, unless the parameters characterising the spacetimes satisfy the constraint we derive and solve in the current paper. In the Kerr-NUT-de Sitter case, the constraint relates the cosmological constant of spacetime and the horizon area, leaving 3 parameters free. In the accelerated case the acceleration becomes a 4th parameter that allows the cosmological constant to take arb…
Bound on Lyapunov exponent in Kerr-Newman-de Sitter black holes by a charged particle
本文结合解析与数值方法，考察带电且带角动量粒子在多种 de Sitter 黑洞及 Nariai、超冷极限下对 Lyapunov 指数界限的影响，发现正宇宙学常数情形仍存在违例。
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