We prove that the most general solution of the Einstein equations with the cosmological constant which admits a principal conformal Killing-Yano tensor is the Kerr-NUT-(A)dS metric. Even when the Einstein equations are not imposed, any spacetime admitting such hidden symmetry can be written in a canonical form which guarantees the following properties: it is of the Petrov type D, it allows the separation of variables for the Hamilton-Jacobi, Klein-Gordon, and Dirac equations, the geodesic motion in such a spacetime is completely integrable. These results naturally generalize the results obtained earlier in four dimensions.
We study a class of limits of the higher-dimensional Kerr-NUT-(A)dS spacetimes where particular roots of metric functions degenerate. Namely, we obtain the Taub-NUT-(A)dS and the extreme near-horizon geometries as two examples of our limiting procedure. The symmetries of the resulting spacetimes are enhanced which is manifested by the presence of supplementary Killing vectors and decomposition of Killing tensors into Killing vectors.
We demonstrate the separability of the Hamilton-Jacobi and scalar field equations in general higher dimensional Kerr-NUT-AdS spacetimes. No restriction on the parameters characterizing these metrics is imposed.
We demonstrate that the general (A)dS-Kerr-NUT solutions in D dimensions with ([D/2], [(D+1)/2]) signature admit [D/2] linearly-independent, mutually-orthogonal and affinely-parameterised null geodesic congruences. This enables us to write the metrics in a multi-Kerr-Schild form, where the mass and all of the NUT parameters enter the metrics linearly. In the case of D=2n, we also obtain n harmonic 2-forms, which can be viewed as charged (A)dS-Kerr-NUT solution at the linear level of small-charge expansion, for the higher-dimensional Einstein-Maxwell theories. In the BPS limit, these 2-forms re…
Motivated by the recent researches of black holes with NUT charge, we investigate the validity of the weak cosmic censorship conjecture for Kerr-Taub-NUT black hole with a test massive scalar field and a test particle, respectively. For the scalar field scattering gedanken experiment, we consider an infinitesimal time interval process. The result shows that both extremal and near-extremal Kerr-Taub-NUT black holes cannot be over-spun. For the test particle thought experiment, the study suggests that extremal Kerr-Taub-NUT black hole cannot be over-spun; while near-extremal Kerr-Taub-NUT black …
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.
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…
It is well known that 4-dimensional Kerr-NUT-AdS spacetime possesses the hidden symmetry associated with the Killing-Yano tensor. This tensor is "universal" in the sense that there exist coordinates where it does not depend on any of the free parameters of the metric. Recently the general higher dimensional Kerr-NUT-AdS solutions of the Einstein equations were obtained. We demonstrate that all these metrics with arbitrary rotation and NUT parameters admit a universal Killing-Yano tensor. We give an explicit presentation of the Killing-Yano and Killing tensors and briefly discuss their properti…
The four-dimensional Kerr-de Sitter and Kerr-AdS black hole metrics have cohomogeneity 2, and they admit a generalisation in which an additional parameter characterising a NUT charge is included. In this paper, we study the higher-dimensional Kerr-AdS metrics, specialised to cohomogeneity 2 by appropriate restrictions on their rotation parameters, and we show how they too admit a generalisation in which an additional NUT-type parameter is introduced. We discuss also the supersymmetric limits of the new metrics. If one performs a Wick rotation to Euclidean spacetime signature, these yield new E…
We study the Hawking thermal spectrum in dragging coordinate system and the tunneling radiation characteristics of hot NUT-Kerr-Newman-Kasuya spacetime. The tunneling rates at the event and cosmological horizon are found to be related to the change of Bekenstein-Hawking entropy. The radiation spectrum is not pure thermal and thus there is a correction to the Hawking thermal spectrum.
We present an exact solution describing a stationary and axisymmetric object with electromagnetic and dilaton fields. The solution generalizes the usual Kerr-Taub-NUT (Newman-Unti-Tamburino) spacetime in general relativity and is obtained by boosting this spacetime in the fifth dimension and performing a Kaluza-Klein reduction to four dimensions. We also discuss the physical parameters of this solution and calculate its gyromagnetic ratio.
We study fixed points of isometries of the higher-dimensional Kerr-NUT-(A)dS spacetimes that form generalizations of symmetry axes. It turns out that, in the presence of nonzero NUT charges, some parts of the symmetry axes are necessarily singular and their intersections are surrounded by regions with closed timelike curves. Motivated by similarities with the spacetime of a spinning cosmic string, we introduce geometric quantities that characterize various types of singularities on symmetry axes. Expanding the Kerr-NUT-(A)dS spacetimes around candidates for possible fixed points, we find the K…
It is well known that the Kerr-NUT-AdS-dS black hole admits two linearly independent Killing vectors and possesses a hidden symmetry generated by a rank-2 Killing tensor. The near-horizon geometry of an extremal Kerr-NUT-AdS-dS black hole admits four linearly independent Killing vectors, and we show how the hidden symmetry of the black hole itself is carried over by means of a modified Killing-Yano potential which is given explicitly. We demonstrate that the corresponding Killing tensor of the near-horizon geometry is reducible as it can be expressed in terms of the Casimir operators formed by…
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…
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 study properties of a recently proposed new ansatz for separation of variables in the Maxwell equations in four dimensional Kerr-NUT-(A)dS spacetime. We demonstrate that a dual field, which is also a solution of the source-free Maxwell equations, can be presented in a similar form. This result implies that the corresponding separated equations possess a discrete symmetry under a special transform of the separation parameters.
Electric-magnetic duality, the Newman-Janis shift, and the double copy all act by elementary operations on three-point amplitudes. At the same time, they generate a network of interesting classical solutions spanning from the Coulomb charge via the dyon to the Kerr-Taub-NUT spacetime. We identify the amplitudes corresponding to each of these solutions, working to all orders in spin, but to leading perturbative order. We confirm that the amplitudes double-copy when the solutions are related by the classical double copy. Along the way we show that the Kerr-Taub-NUT solution corresponds to a grav…
We find an explicit solution of the source free Maxwell equations in a generalized Kerr-NUT-(A)dS spacetime in all dimensions. This solution is obtained as a linear combination of the closed conformal Killing-Yano tensor $h_{ab}$, which is present in such a spacetime, and a derivative of the primary Killing vector, associated with $h_{ab}$. For the vanishing cosmological constant the obtained solution reduces to the Wald's electromagnetic field generated from the primary Killing vector.
In this work, we perform a detailed analysis of the equatorial motion of the charged test particles in Kerr-Newman-Taub-NUT spacetime. By working out the orbit equation in the radial direction, we examine possible orbit types. We investigate the conditions for existence of bound orbits in causality-preserving region as well as the conditions for existence of circular orbits for charged and uncharged particles. We also study the effect of NUT parameter on Newtonian orbits. Finally, we give exact analytical solutions of equations of equatorial motion for a charged test particle.
We study the collision of two particles with the different rest masses moving in the equatorial plane of a Kerr-Taub-NUT spacetime and get the center-of-mass (CM) energy for the particles. We find that the CM energy depends not only on the rotation parameter, $a$, but also on the NUT charge of the Kerr-Taub-NUT spacetime, $n$. Especially, for the extremal Kerr-Taub-NUT spacetime, an unlimited CM energy can be approached if the parameter $a$ is in the range $[1,\sqrt{2}]$, which is different from that of the Kerr and Kerr-Newman black holes.
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 Kerr-AdS metric in dimension D has cohomogeneity [D/2]; the metric components depend on the radial coordinate r and [D/2] latitude variables μ_i that are subject to the constraint \sum_i μ_i^2=1. We find a coordinate reparameterisation in which the μ_i variables are replaced by [D/2]-1 unconstrained coordinates y_α, and having the remarkable property that the Kerr-AdS metric becomes diagonal in the coordinate differentials dy_α. The coordinates r and y_αnow appear in a very symmetrical way in the metric, leading to an immediate generalisation in which we can introduce [D/2]-1 NUT parameter…
The duality relating the four-dimensional Kerr-Taub-NUT black hole to a thermal two-dimensional CFT with central charges $c_L=c_R=12 J_0$ is analyzed in detail, generalizing an argument given recently for Kerr within the soft-hair approach. The hidden conformal symmetry is realized in the form of $Vir_L \times Vir_R$ diffeomorphisms which act non-trivially on the black hole horizon. Semiclassical formulae are derived for the temperature and central charges of the dual CFT. Assuming the applicability of the Cardy formula, these CFT quantities precisely reproduce the macroscopic Bekenstein-Hawki…
We investigate properties of higher-dimensional generally rotating black-hole spacetimes, so called Kerr-NUT-(A)dS spacetimes, as well as a family of related spaces which share the same explicit and hidden symmetries. In these spaces, we study a particle motion in the presence of a weak electromagnetic field and compare it with its operator analogies. First, we find general commutativity conditions for classical observables and for their operator counterparts, then we investigate a fulfillment of these conditions in the Kerr-NUT-(A)dS and related spaces. We find the most general form of the we…
We construct a new class of vacuum black hole solutions whose geometry is deformed and twisted by the presence of NUT charges. The solutions are obtained by `unspinning' the general Kerr-NUT-(A)dS spacetimes, effectively switching off some of their rotation parameters. The resulting geometry has a structure of warped space with the Kerr-like Lorentzian part warped to a Euclidean metric of deformed and/or twisted sphere, with the deformation and twist characterized by the `Euclidean NUT' parameters. In the absence of NUTs, the solution reduces to a well known Kerr-(A)dS black hole with several …
In this work, we study the motion of charged test particles in Kerr-Newman-Taub-NUT spacetime. We analyze the angular and the radial parts of the orbit equations and examine the possible orbit types. We also investigate the spherical orbits and their stabilities. Furthermore, we obtain the analytical solutions of the equations of motion and express them in terms of Jacobian and Weierstrass elliptic functions. Finally, we discuss the observables of the bound motion and calculate the perihelion shift and Lense-Thirring effect for three dimensional bound orbits.
We demonstrate complete integrability of the Nambu-Goto equations for a stationary string in the general Kerr-NUT-(A)dS spacetime describing the higher-dimensional rotating black hole. The stationary string in D dimensions is generated by a 1-parameter family of Killing trajectories and the problem of finding a string configuration reduces to a problem of finding a geodesic line in an effective (D-1)-dimensional space. Resulting integrability of this geodesic problem is connected with the existence of hidden symmetries which are inherited from the black hole background. In a spacetime with p m…
The remarkable and unexpected separability of the Hamilton-Jacobi and Klein-Gordon equations in the background of a rotating four-dimensional black hole played an important role in the construction of generalisations of the Kerr metric, and in the uncovering of hidden symmetries associated with the existence of Killing tensors. In this paper, we show that the Hamilton-Jacobi and Klein-Gordon equations are separable in Kerr-AdS backgrounds in all dimensions, if one specialises the rotation parameters so that the metrics have cohomogeneity 2. Furthermore, we show that this property of separabili…
In this paper, we investigate the strong gravitational lensing by the stationary, axially-symmetric black hole in Kerr-Taub-NUT spacetime in the strong field limit. The deflection angle of light ray and other strong deflection limit coefficients are obtained numerically and they are found to be closely dependent on the NUT charge $n$ and spin $a$. The magnification and the positions of the relativistic images are computed. The caustics are studied and the results show that these caustics drift away from the optical axis, which is quite different from the Schwarzschild black hole case. Moreover…
We study how gravitational duality acts on rotating solutions, using the Kerr-NUT black hole as an example. After properly reconsidering how to take into account both electric (i.e. mass-like) and magnetic (i.e. NUT-like) sources in the equations of general relativity, we propose a set of definitions for the dual Lorentz charges. We then show that the Kerr-NUT solution has non-trivial such charges. Further, we clarify in which respect Kerr's source can be seen as a mass M with a dipole of NUT charges.
We extend the topological Kerr-Newman-aDS solutions by including NUT charge and find generalizations of the Robinson-Bertotti solution to the negative cosmological constant case with different topologies. We show how all these solutions can be obtained as limits of the general Plebanski-Demianski solution. We study the supersymmetry properties of all these solutions in the context of gauged N=2,d=4 supergravity. Generically they preserve at most 1/4 of the total supersymmetry. In the Plebanski-Demianski case, although gauged N=2,d=4 supergravity does not have electric-magnetic duality, we find…
Generalizing the scaling limit of Martelli and Sparks [hep-th/0505027] into an arbitrary number of spacetime dimensions we re-obtain the (most general explicitly known) Einstein-Sasaki spaces constructed by Chen, Lu, and Pope [hep-th/0604125]. We demonstrate that this limit has a well-defined geometrical meaning which links together the principal conformal Killing-Yano tensor of the original Kerr-NUT-(A)dS spacetime, the Kahler 2-form of the resulting Einstein-Kahler base, and the Sasakian 1-form of the final Einstein-Sasaki space. The obtained Einstein-Sasaki space possesses the tower of Kill…
We obtain and study the equations describing the parallel transport of orthonormal frames along geodesics in a spacetime admitting a non-degenerate principal conformal Killing-Yano tensor h. We demonstrate that the operator F, obtained by a projection of h to a subspace orthogonal to the velocity, has in a generic case eigenspaces of dimension not greater than 2. Each of these eigenspaces are independently parallel-propagated. This allows one to reduce the parallel transport equations to a set of the first order ordinary differential equations for the angles of rotation in the 2D eigenspaces. …
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…
We present a new twisted rotating black hole solution by performing Demia{ń}ski-Newman-Janis algorithm to the electrically and dyonically charged black hole with quintessence in Rastall theory of gravity. Using our black hole solution, we argue that Rastall gravity is not equivalent with Einstein gravity. For further explanation, the black hole properties such as the horizon and ergosphere are studied for which there are some different properties for those theories. Some thermodynamic properties of the black hole solution are also discussed. At the end, considering the Kerr/CFT correspondence …
We study the Hawking radiation as charged particles' tunneling across the horizons of the Hot-NUT-Kerr-Newman-Kasuya spacetime by considering the spacetime background as dynamical and incorporating the self-gravitation effect of the emitted particles when the energy conservation, the angular momentum conservation, and the electric charge conservation are taken into account. Our result shows that the tunneling rate is related to the change of Bekenstein-Hawking entropy and the radiant spectrum is not pure thermal, but is consistent with an underlying unitary theory. The emission process is a re…
We derive the multipole moments of the Kerr-NUT black hole spacetime using the Geroch-Hansen formalism, even though the spacetime is not asymptotically flat. Intriguingly, in the presence of the NUT charge, the absence of reflection symmetry about the equatorial plane, leads to mass and spin multipole moments of all orders, in stark contrast to Kerr-like spacetimes. This leads to a drastic departure of the multipolar structure of a compact object with NUT charge, whose implications for gravitational wave observations have been explored. Our analysis of multipole moments for the Kerr-NUT spacet…
We intrinsically characterize separability of the Dirac equation in Kerr-NUT-(A)dS spacetimes in all dimensions. Namely, we explicitly demonstrate that in such spacetimes there exists a complete set of first-order mutually commuting operators, one of which is the Dirac operator, that allows for common eigenfunctions which can be found in a separated form and correspond precisely to the general solution of the Dirac equation found by Oota and Yasui [arXiv:0711.0078]. Since all the operators in the set can be generated from the principal conformal Killing-Yano tensor, this establishes the (up to…
In this work we have presented a special class of Kerr-Newman-NUT black hole, having its horizon located precisely at $r=2M$, for $Q^{2}=l^{2}-a^{2}$, where $M$, $l$, $a$ and $Q$ are respectively mass, NUT, rotation and electric charge parameters of the black hole. Clearly this choice radically alters the causal structure as there exists no Cauchy horizon indicating spacelike nature of the singularity when it exists. On the other hand, there is no curvature singularity for $l^2 > a^2$, however it may have conical singularities. Furthermore there is no upper bound on specific rotation parameter…
We present exact non-singular bounce solutions of general relativity in the presence of a positive cosmological constant and an electromagnetic field, without any exotic matter. The solutions are distinguished by being spatially inhomogeneous in one direction, while they can also contain non-trivial electromagnetic field lines. The inhomogeneity may be substantial, for instance, there can be one bounce in one region of the universe and two bounces elsewhere. Since the bounces are followed by a phase of accelerated expansion, the metrics described here also permit the study of (geodesically com…
We explicitly exhibit n-1 constants of motion for geodesics in the general D-dimensional Kerr-NUT-AdS rotating black hole spacetime, arising from contractions of even powers of the 2-form obtained by contracting the geodesic velocity with the dual of the contraction of the velocity with the (D-2)-dimensional Killing-Yano tensor. These constants of motion are functionally independent of each other and of the D-n+1 constants of motion that arise from the metric and the D-n = [(D+1)/2] Killing vectors, making a total of D independent constants of motion in all dimensions D. The Poisson brackets o…
Rotating black hole solution surrounded by quintessential matter is recently discussed because it might be the promising solution to study the effect of dark energy in small scale of the universe. This quintessential solution is originally derived from the condition of additivity and linearity for the energy-momentum tensor. We carry out the thermodynamic properties of this solution using the Kerr/CFT correspondence for several specific quintessential equation of state parameters. A problem arises when we compute the central charge because the canonical conserved charge is needed to be calcula…
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.
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.
We investigate the Kerr-Newman-NUT black hole solution obtained from Plebański-Demiański solutions with several assumptions. The origin of the microscopic entropy of this black hole is investigated using the conjectured Kerr/CFT correspondence which is originally proposed for extremal Kerr black holes. The isometry of the near-horizon extremal Kerr-Newman-NUT black hole shows that the asymptotic symmetry group may be implemented to compute the central charge of the Virasoro algebra. Furthermore, by assuming Frolov-Thorne vacuum, the conformal temperatures can be obtained. Then by using the Car…
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.
The duality between the original Kaluza's theory and Klein's subsequent modification is duality between slicing and threading decomposition of the five-dimensional spacetime. The field equations of the original Kaluza's theory lead to the interpretation of the four-dimensional Lorentzian Kerr and Taub--NUT solutions as resulting from static electric and magnetic charges and dipoles in the presence of ghost matter and constant dilaton, which models Newton's constant.
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…
