The near horizon geometries are usually constructed by implementing a specific limit to a given extreme black hole configuration. Their salient feature is that the isometry group includes the conformal subgroup SO(2,1). In this work, we turn the logic around and use the conformal invariants for constructing Ricci-flat metrics in d=4 and d=5 where the vacuum Einstein equations reduce to a coupled set of ordinary differential equations. In four dimensions the analysis can be carried out in full generality and the resulting metric describes the d=4 near horizon Kerr-NUT black hole. In five dimensions we choose a specific ansatz whose structure is similar to the d=5 near horizon Myers-Perry black hole. A Ricci-flat metric involving five arbitrary parameters is constructed. A particular member of this family, which is characterized by three parameters, seems to be a natural candidate to describe the d=5 near horizon Myers-Perry black hole with a NUT charge.
We study the spectrum of Laplace operators on a one-parameter family of gravitational instantons of bi-axial Bianchi IX type coupled to an abelian connection with self-dual curvature. The family of geometries includes the Taub-NUT, Taub-bolt and Euclidean Schwarzschild geometries and interpolates between them. The interpolating geometries have conical singularities along a submanifold of co-dimension two, but we prove that the associated Laplace operators have natural self-adjoint extensions and study their spectra. In particular, we determine the essential spectrum and prove that its compleme…
We obtain $D_k$ ALF gravitational instantons by a gluing construction which captures, in a precise and explicit fashion, their interpretation as non-linear superpositions of the moduli space of centred $SU(2)$ monopoles, equipped with the Atiyah-Hitchin metric, and $k$ copies of the Taub-NUT manifold. The construction proceeds from a finite set of points in euclidean space, reflection symmetric about the origin, and depends on an adiabatic parameter which is incorporated into the geometry as a fifth dimension. Using a formulation in terms of hyperKähler triples on manifolds with boundaries, we…
In this paper, we construct new solutions describing rotating black rings on Taub-NUT using the inverse-scattering method. These are five-dimensional vacuum space-times, generalising the Emparan-Reall and extremal Pomeransky-Sen'kov black rings to a Taub-NUT background space. When reduced to four dimensions in Kaluza-Klein theory, these solutions describe (possibly rotating) electrically charged black holes in superposition with a finitely separated magnetic monopole. Various properties of these solutions are studied, from both a five- and four-dimensional perspective.
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…
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 address a long-standing problem of describing the thermodynamics of rotating Taub--NUT solutions. The obtained first law is of full cohomogeneity and allows for asymmetric distributions of Misner strings as well as their potential variable strengths---encoded in the gravitational Misner charges. Notably, the angular momentum is no longer given by the Noether charge over the sphere at infinity and picks up non-trivial contributions from Misner strings.
We show that the first law for the rotating Taub-NUT is straightforwardly established with the surface charge method. The entropy is explicitly found as a charge, and its value is not proportional to the horizon area. We conclude that there are unavoidable contributions from the Misner strings to the charges, still, the mass and angular momentum gets standard values. However, there are no independent charges associated with the Misner strings.
We study the quantum tunneling of scalars from charged accelerating and rotating black hole with NUT parameter. For this purpose we use the charged Klein-Gordon equation. We apply WKB approximation and the Hamilton-Jacobi method to solve charged the Klein-Gordon equation. We find the tunneling probability of outgoing charged scalars from the event horizon of this black hole, and hence the Hawking temperature for this black hole.
In this work, we generalized the Kerr-Newman-NUT black hole solution in Rastall gravity from Ref. 1. Here we are more focused on the black hole dynamics such as the event horizons, ergosurface, ZAMO, thermodynamic properties, and the equatorial circular orbit around the black hole such as static radius limit, null equatorial circular orbit, and innermost stable circular orbit. We present how the NUT and Rastall parameter affects the dynamic of the black hole.
A global solution of the Einstein equations is given, consisting of a perfect fluid interior and a vacuum exterior. The rigidly rotating and incompressible perfect fluid is matched along the hypersurface of vanishing pressure with the stationary part of the Taub-NUT metric. The fluid core generates a negative-mass NUT space-time. The matching procedure leaves one parameter in the global solution.
Locally rotationally symmetric perfect fluid solutions of Einstein's gravitational equations are matched along the hypersurface of vanishing pressure with the NUT metric. These rigidly rotating fluids are interpreted as sources for the vacuum exterior which consists only of a stationary region of the Taub-NUT space-time. The solution of the matching conditions leaves generally three parameters in the global solution. Examples of perfect fluid sources are discussed.
This paper is devoted to the study of Hawking radiation as a tunneling of charged fermions through event horizons of a pair of charged accelerating and rotating black holes with NUT parameter. We evaluate tunneling probabilities of outgoing charged particles by using the semiclassical WKB approximation to the general covariant Dirac equation. The Hawking temperature corresponding to this pair of black holes is also investigated. For the zero NUT parameter, we find results consistent with those already available in the literature.
We extend the work on thermodynamics of Lorentzian NUTty solutions, by including simultaneously the effect of rotation and electromagnetic charges. Due to the fact that Misner strings carry electric charge, and similar to the non-rotating case, we observe an interesting interplay between the horizon and asymptotic charges. Namely, upon employing the Euclidean action calculation we derive two alternative full cohomogeneity first laws, one that includes the variations of the horizon electric charge and the asymptotic magnetic charge and another that involves the horizon magnetic charge and the a…
We consider four dimensional stationary and axially symmetric spacetimes for conformally coupled scalar-tensor theories. We show that, in analogy to the Lewis-Papapetrou problem in General Relativity (GR), the theory at hand can be recast in an analogous integrable form. We give the relevant rod formalism, introduced by Weyl for vacuum GR, explicitly giving the rod structure of the black hole of Bocharova et al. and Bekenstein (BBMB), in complete analogy to the Schwarzschild solution. The additional scalar field is shown to play the role of an extra Weyl potential. We then employ the Ernst met…
In this review we present the most general form of the Janis--Newman algorithm. This extension allows to generate configurations which contain all bosonic fields with spin less than or equal to two (real and complex scalar fields, gauge fields, metric field) and with five of the six parameters of the Plebański-Demiański metric (mass, electric charge, magnetic charge, NUT charge and angular momentum). Several examples are included to illustrate the algorithm. We also discuss the extension of the algorithm to other dimensions.
We study the solutions of the Euclidean-signature Einstein equations (gravitational instantons) whose line-element takes the Kerr-bolt form, characterized by three real parameters: a size, a NUT charge, and a spin rate. The exclusion of singularities eliminates most combinations of these parameters, leaving only separated solution-manifolds between which continuous transitions are impossible (The angular velocity divided by the temperature is forced to be a rational multiple of $2π$). This ``quantization'' prevents the free variations presupposed by an equation like $T dS=dM + ΩdJ$, and thereb…
General relativistic quantum interference effects in the slowly rotating NUT space-time as the Sagnac effect and the phase shift effect of interfering particle in neutron interferometer are considered. It was found that in the case of the Sagnac effect the influence of NUT parameter is becoming important due to the fact that the angular velocity of the locally non rotating observer must be larger than one in the Kerr space-time. In the case of neutron interferometry it is found that due to the presence of NUT-parameter an additional term in the phase shift of interfering particle emerges. This…
Rotating disks with nonzero radial pressure and finite radius are studied. The models are based in the Taub-NUT metric and constructed using the well-known ``displace, cut and reflect'' method. We find that the disks are made of perfect fluids with constant energy density and pressure. The energy density is negative, but the effective Newotnian density is possitive as the strong energy condition requires. We also find that the disks are not stable under radial perturbations and that there are regions of the disks where the particles move with superluminal velocities.
We construct novel solutions to the effective Einstein equation with four dimensional cosmological constant on a 3-brane in Randall-Sundrum II scenario. The charged solution is obtained by assuming the existence of localized Maxwell fields on the 3-brane. Timelike and null circular geodesics in the neutral rotating braneworld spacetime with NUT parameter are discussed, and we find that such geodesics cannot occur on the equatorial plane. On non-equatorial planes, timelike circular geodesics can occur for the negative tidal charge, but we cannot find numerical results to support the existence o…
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…
The double copy is a much-studied relationship between gauge theory and gravity amplitudes. Recently, this was generalised to an infinite family of classical solutions to Einstein's equations, namely stationary Kerr-Schild geometries. In this paper, we extend this to the Taub-NUT solution in gravity, which has a double Kerr-Schild form. The single copy of this solution is a dyon, whose electric and magnetic charges are related to the mass and NUT charge in the gravity theory. Finally, we find hints that the classical double copy extends to curved background geometries.
A family of models of counterrotating and rotating relativistic thin discs of infinite extension based on a charged and magnetized Kerr-NUT metric are constructed using the well-known "displace, cut and reflect" method extended to solutions of vacuum Einstein-Maxwell equations. The metric considered has as limiting cases a charged and magnetized Taub-NUT solution and the well known Kerr-Newman solutions. We show that for Kerr-Newman fields the eigenvalues of the energy-momentum tensor of the disc are for all the values of the parameters real quantities so that these discs do not present heat f…
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.
The exact solution for the electromagnetic field occuring when the Kerr-Taub-NUT compact object is immersed (i) in an originally uniform magnetic field aligned along the axis of axial symmetry (ii) in dipolar magnetic field generated by current loop has been investigated. Effective potential of motion of charged test particle around Kerr-Taub-NUT gravitational source immersed in magnetic field with different values of external magnetic field and NUT parameter has been also investigated. In both cases presence of NUT parameter and magnetic field shifts stable circular orbits in the direction of…
Thermodynamics of a large family of black holes from electrovacuum solutions of Einstein's equations is studied. This family includes rotating and non-accelerating black holes with NUT charge, and rotating and accelerating black holes. The surface gravity, Hawking temperature and the area laws for these black holes are presented. The first law of thermodynamics is also given. An interesting outcome of our analysis is the restriction obtained on the magnitude of acceleration for these black holes.
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…
An exact solution of Einstein's equations which represents a pair of accelerating and rotating black holes (a generalised form of the spinning C-metric) is presented. The starting point is a form of the Plebanski-Demianski metric which, in addition to the usual parameters, explicitly includes parameters which describe the acceleration and angular velocity of the sources. This is transformed to a form which explicitly contains the known special cases for either rotating or accelerating black holes. Electromagnetic charges and a NUT parameter are included, the relation between the NUT parameter …
The classical boundary-value problem of the Einstein field equations is studied with an arbitrary cosmological constant, in the case of a compact ($S^{3}$) boundary given a biaxial Bianchi-IX positive-definite three-metric, specified by two radii $(a,b).$ For the simplest, four-ball, topology of the manifold with this boundary, the regular classical solutions are found within the family of Taub-NUT-(anti)de Sitter metrics with self-dual Weyl curvature. For arbitrary choice of positive radii $(a,b),$ we find that there are three solutions for the infilling geometry of this type. We obtain exact…
In this thesis we study higher-dimensional rotating black holes. Such black holes are widely discussed in string theory and brane-world models at present. We demonstrate that even the most general known Kerr-NUT-(A)dS spacetime, describing the general rotating higher-dimensional asymptotically (anti) de Sitter black hole with NUT parameters, is in many aspects similar to its four-dimensional counterpart. Namely, we show that it admits a fundamental hidden symmetry associated with the principal conformal Killing-Yano tensor. Such a tensor generates towers of hidden and explicit symmetries. The …
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…
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 paper we show that an isolated Kerr black hole can be interpreted as arising from a pair of identical counter-rotating NUT objects placed on the symmetry axis at an appropriate distance from each other.
We solve the recently-proposed equations describing non-BPS extremal multi-center configurations, and construct explicit solutions describing non-supersymmetric extremal black rings in Taub-NUT, as well as the seed solution for the most general extremal non-BPS under-rotating black hole in four dimensions. We also find solutions that contain both a black hole and a black ring, which descend to four-dimensional extremal non-BPS two-center black holes with generic charges.
We study Maxwell equations in the external background spacetime of a slowly rotating magnetized NUT star and find analytical solutions for the exterior electric fields after separating the equations of electric field into angular and radial parts in the lowest order approximation. The star is considered isolated and in vacuum, with dipolar magnetic field aligned with the axis of rotation. The contribution to the external electric field of star from the NUT charge is considered in detail.
We present covariant symmetry operators for the conformal wave equation in the (off-shell) Kerr-NUT-AdS spacetimes. These operators, that are constructed from the principal Killing-Yano tensor, its `symmetry descendants', and the curvature tensor, guarantee separability of the conformal wave equation in these spacetimes. We next discuss how these operators give rise to a full set of conformally invariant mutually commuting operators for the conformally rescaled spacetimes and underlie the $R$-separability of the conformal wave equation therein. Finally, by employing the WKB approximation we de…
We present a new family of exact four-dimensional Taub-NUT spacetimes in Einstein-$Λ$ theory supplemented with a conformally coupled scalar field exhibiting a power-counting super-renormalizable potential. The construction proceeds as follows: A solution of a conformally coupled theory with a conformal potential, henceforth the seed $(g_{μν},ϕ)$, is transformed by the action of a specific change of frame in addition with a simultaneous shift of the seed scalar. The new configuration, $(\bar{g}_{μν},\barϕ)$, solves the field equations of a conformally coupled theory with the aforementioned supe…
We present a slowly rotating generalization of a black hole modeled by a Solv horizon geometry, in five dimensional General Relativity. A separable ansatz compatible with Einstein equations is proposed, which is integrated in terms of hypergeometric and exponential functions. The solution highly simplifies after requiring to maintain the same asymptotic behaviour as the non-rotating black hole and to have finite, non-vanishing charges. We compute the charges of the solution and also comment on its importance for studying the phase space of the theory in this sector.
We have obtained the most general solution of the Einstein vacuum equation for the axially symmetric stationary metric in which both the Hamilton-Jacobi equation for particle motion and the Klein - Gordon equation are separable. It can be interpreted to describe the gravitational field of a rotating dyon, a particle endowed with both gravoelectric (mass) and gravomagnetic (NUT parameter) charge. Further, there also exists a duality relation between the two charges and the radial and the polar angle coordinates which keeps the solution invariant. The solution can however be transformed into the…
We present a novel solution obeying classical equation of motion in the low energy limit of heterotic string theory. The solution represents a rotating mass with electric charge and gravitomagnetic monopole moment. The corresponding conserved charges are discussed. We also study the test body circular equatorial motions in the spacetime.
We derive a correspondence between the Hawking radiation spectra emitted from general classes of Taub-NUT black holes with that induced by the relativistic motion of an accelerated Dirichlet boundary condition (i.e.\ a perfectly reflecting mirror) in (1+1)-dimensional flat spacetime. We demonstrate that the particle and energy spectra is thermal at late-times and that particle production is suppressed by the NUT parameter. We also compute the radiation spectrum in the rotating, electrically charged (Kerr-Newman) Taub-NUT scenario, and the extremal case, showing explicitly how these parameters …
We study the thermodynamics and the thermodynamic geometries of charged rotating BTZ (CR-BTZ) black holes in (2+1)-gravity. We investigate the thermodynamics of these systems within the context of the Weinhold and Ruppeiner thermodynamic geometries and the recently developed formalism of geometrothermodynamics (GTD). Considering the behavior of the heat capacity and the Hawking temperature, we show that Weinhold and Ruppeiner geometries cannot describe completely the thermodynamics of these black holes and of their limiting case of vanishing electric charge. In contrast, the Legendre invarianc…
We consider stationary extremal black hole solutions of the Einstein-Maxwell equations with a negative cosmological constant in four dimensions. We determine all non-static axisymmetric near-horizon geometries (with non-toroidal horizon topology) and all static near-horizon geometries for black holes of this kind. This allows us to deduce that the most general near-horizon geometry of an asymptotically globally AdS(4) rotating extremal black hole, is the near-horizon limit of extremal Kerr-Newman-AdS(4). We also identify the subset of near-horizon geometries which are supersymmetric. Finally, …
We study magnetospheric structure surrounding rotating magnetized neutron star with nonvanishing NUT (Newman-Tamburino-Unti) parameter. For the simplicity of calculations Goldreich-Julian charge density is analyzed for the aligned neutron star with zero inclination between magnetic field, gravitomagnetic field and rotation axis. From the system of Maxwell equations in spacetime of slowly rotating NUT star, second-order differential equation for electrostatic potential is derived. Analytical solution of this equation indicates the general relativistic modification of an accelerating electric fi…
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 consider four-dimensional U(1)^4 gauged supergravity, and obtain asymptotically AdS_4, non-extremal, charged, rotating black holes with one non-zero U(1) charge. The thermodynamic quantities are computed. We obtain a generalization that includes a NUT parameter. The general solution has a discrete symmetry involving inversion of the rotation parameter, and has a string frame metric that admits a rank-2 Killing-Stackel tensor.
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…
We study the integrability of geodesic flow in the background of some recently discovered charged rotating solutions of supergravity in four and five dimensions. Specifically, we work with the gauged multicharge Taub-NUT-Kerr-(Anti) de Sitter metric in four dimensions, and the $U(1)^3$ gauged charged-Kerr-(Anti) de Sitter black hole solution of N = 2 supergravity in five dimensions. We explicitly construct the Killing tensors that permit separation of the Hamilton-Jacobi equation in these spacetimes. These results prove integrability for a large class of previously known supergravity solutions…
