Sergey A. Cherkis
We present a construction of self-dual Yang-Mills connections on the Taub-NUT space. We illustrate it by finding explicit expressions for all SU(2) instantons of instanton number one and generic monodromy at infinity.
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We study finite action anti-self-dual Yang-Mills connections on the multi-Taub-NUT space. We establish the curvature and the harmonic spinors decay rates and compute the index of the associated Dirac operator. This is the first in a series of papers proving the completeness of the bow construction of instantons on multi-Taub-NUT spaces and exploring it in detail.
We present ADHM-Nahm data for instantons on the Taub-NUT space and encode these data in terms of Bow Diagrams. We study the moduli spaces of the instantons and present these spaces as finite hyperkahler quotients. As an example, we find an explicit expression for the metric on the moduli space of one SU(2) instanton. We motivate our construction by identifying a corresponding string theory brane configuration. By following string theory dualities we are led to supersymmetric gauge theories with impurities.
Instantons on multi-Taub-NUT Spaces III: Down Transform, Completeness, and Isometry
本文研究多 Taub-NUT 空间上的瞬子，利用相关 Dirac 算子族的指标丛所形成的 bow 表示，证明其规范等价类与瞬子一一对应，并给出两模空间间的等距。
ALE and Taub-NUT (or ALF) hyper-Kahler four-manifolds can be naturally constructed as hyper-Kahler quotients. In the ALE case, this construction has long been understood in terms of D-branes; here we give a D-brane derivation in the Taub-NUT case. Likewise, instantons on ALE spaces and on Taub-NUT spaces have ADHM-like constructions related to hyper-Kahler quotients. Here we refine the analysis in the Taub-NUT case by making use of a D-brane probe, and give an application to M-theory.
We consider a finite action for a higher dimensional Taub-NUT/Bolt-(A)dS space via the so-called counter term subtraction method. In the limit of high temperature, we show that the Cardy-Verlinde formula holds for the Taub-Bolt-AdS metric and for the specific dimensional Taub-NUT-(A)dS metric, except for the Taub-Bolt-dS metric.
Higher-spins on Taub-NUT and higher-spin Taub-NUT
本文研究自对偶杨-米尔斯和自对偶引力的高自旋扩展，在Taub-NUT背景上构造精确解，并给出高自旋Taub-NUT的微扰推广及其代数结构。
We present a class of higher dimensional solutions to Einstein-Maxwell equations in d-dimensions. These solutions are asymptotically locally flat, de-Sitter, or anti-de Sitter space-times. The solutions we obtained depend on two extra parameters other than the mass and the nut charge. These two parameters are the electric charge, q and the electric potential at infinity, V, which has a non-trivial contribution. We Analyze the conditions one can impose to obtain Taub-Nut or Taub-Bolt space-times, including the four-dimensional case. We found that in the nut case these conditions coincide with t…
Using chiral supersymmetry, we show that the massless Dirac equation in the Taub-NUT gravitational instanton field is exactly soluble and explain the arisal and the use of the dynamical (super) symmetry.
We investigate the extended thermodynamic properties of higher-dimensional Taub-NUT/Bolt-AdS spaces where a cosmological constant is treated as a pressure. We find a general form for thermodynamic volumes of Taub-NUT/Bolt-AdS black holes for arbitrary dimensions. Interestingly, it is found that the Taub-NUT-AdS metric has a thermodynamically stable range when the total number of dimensions is a multiple of 4 (4, 8, 12, ...). We also explore their phase structure and find the first order phase transition holds for higher-dimensional cases.
Supersymmetry and the Geometry of Taub-NUT
Taub-NUT空间的超对称扩张允许4个标准超对称和几个额外的非标准超对称。这些对称性的几何起源跟踪。这一结果可应用于引力瞬子中的费米子模以及长距离引力瞬子动力学。
We use the harmonic space technique to construct explicitly a quaternionic extension of the Taub-NUT metric. It depends on two parameters, the first being the Taub-NUT `mass' and the second one the cosmological constant.
We construct the most generic three-charge, three-dipole-charge, BPS black-ring solutions in a Taub-NUT background. These solutions depend on seven charges and six moduli, and interpolate between a four-dimensional black hole and a five-dimensional black ring. They are also instrumental in determining the correct microscopic description of the five-dimensional BPS black rings.
Generalized Runge-Lenz Vector in Taub-Nut Spinning Space
研究了广义Killing方程和Taub-NUT自旋空间的对称性。对于无自旋粒子，龙格-伦茨矢量直接定义了一个运动常数，而对于自旋粒子，它现在需要自旋的非平凡贡献。对自旋Taub-NUT空间的广义Runge-Lenz向量进行了完整的计算。
Stringy Twists of the Taub--Nut Metric
在低能极限，弦论有两个显著的对称性，O（d，d+p）和SL（2，R）。我们说明了使用这些转换的技术，以产生新的解决方案，通过将它们应用到Taub-NUT度量。
We present further analysis of an anisotropic, non-singular early universe model that leads to the viable cosmology presented in Dechant et al (arXiv:0809.4335). Although this model (the DLH model) contains scalar field matter, it is reminiscent of the Taub-NUT vacuum solution in that it has biaxial Bianchi IX geometry and its evolution exhibits a dimensionality reduction at a quasi-regular singularity that one can identify with the big-bang. We show that the DLH and Taub-NUT metrics are related by a coordinate transformation, in which the DLH time coordinate plays the role of conformal time f…
We present an exact solution to the 5D Einstein-Maxwell-dilaton equations describing a static black hole on Taub-Nut instanton. By construction the solution does not possess a charge, but is magnetized along the compact dimension. As a limit we obtain a new regular solution representing a magnetized Kaluza- Klein monopole. We investigate the relevant physical properties and derive the Smarr-like relations.
New Taub-NUT Black Holes with Massive Spin-2 Hair
本文在含二次曲率不变量的爱因斯坦引力中，通过分析Taub-NUT背景的不稳定Lichnerowicz模式确定参数区域，并数值构造出从Ricci-flat解分岔的具有大质量自旋-2毛发的新Taub-NUT黑洞，发现在适当温度下可共存三个黑洞。
The geodesic motion of pseudo-classical spinning particles in Euclidean Taub-NUT space is analysed. The constants of motion are expressed in terms of Killing-Yano tensors. Some previous results from the literature are corrected.
Using the harmonic superspace formalism, we find the metric of a certain 8-dimensional manifold. This manifold is not compact and represents an 8-dimensional generalization of the Taub-NUT manifold. Our conjecture is that the metric that we derived is equivalent to the known metric possessing a discrete $Z_2$ isometry, which may be obtained from the metric describing the dynamics of four BPS monopoles by Hamiltonian reduction.
Newman-Janis Algorithm from Taub-NUT Instantons
本文展示Kerr度规是自对偶与反自对偶Taub-NUT瞬间子的非线性叠加，推动Newman-Janis算法成为具有明确物理起源的Kerr度规推导方法。
We study aspects of the extended gravitational thermodynamics for the Taub-NUT and Taub-Bolt geometries in four dimensional locally anti-de Sitter spacetime, where the cosmological constant is treated as a dynamical pressure. Attention is paid to the phase structure in the (p,T) plane, which has a line of first order phase transitions extending from the origin. We argue for a dynamical interpretation of the unstable physics in the negative specific heat region. A deformation corresponding to a dyonic Taub-NUT/Bolt system is also explored, and the effect of the deformation on the phase diagram …
In this paper we study a solution of heterotic string theory corresponding to a rotating Kerr-Taub-NUT spacetime. It has an exact CFT description as a heterotic coset model, and a Lagrangian formulation as a gauged WZNW model. It is a generalisation of a recently discussed stringy Taub-NUT solution, and is interesting as another laboratory for studying the fate of closed timelike curves and cosmological singularities in string theory. We extend the computation of the exact metric and dilaton to this rotating case, and then discuss some properties of the metric, with particular emphasis on the …
Accelerating Kerr-Taub-NUT spacetime in the low energy limit of heterotic string theory
本研究在杂化弦理论低能极限下构建了带NUT参数的加速带电旋转黑洞新解，分析其视界、能层等时空特性，发现部分特性与加速Kerr-Newman-Taub-NUT时空相似。
I show that there are no SU(2)-invariant (time-dependent) tensorial perturbations of Lorentzian Taub-NUT space. It follows that the spacetime is unstable at the linear level against generic perturbations. I speculate that this fact is responsible for so far unsuccessful attempts to define a sensible thermodynamics for NUT-charged spacetimes.
Exact Analytical Taub-NUT like Solution in f(T) Gravity
本文在 f(T) 引力框架下构造精确解析的类 Taub-NUT 解，分析其物理性质，并与 Einstein 引力对应解比较。
The Geodesic Motion on Generalized Taub-Nut Gravitational Instantons
在耦合到非线性西格玛模型的五维爱因斯坦引力场中，报道了一类广义Taub-NUT引力瞬子.研究了单位质量无自旋粒子在这些静态引力瞬子上的测地线动力学。这是通过找到一个广义的龙格-伦茨矢量来实现的。不像开普勒问题，或者说，一个无自旋粒子在熟悉的陶布-努特引力瞬子上的动力学，轨道不是圆锥截面。
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.
Generalized Killing equations and Taub-NUT spinning space
本文分析了自旋粒子位形空间（自旋空间）的广义Killing方程。这些方程的齐次部分的简单解用Killing-Yano张量表示。一般结果适用于四维欧氏Taub-NUT流形的情况。
We consider the Gibbons-Hawking metric for a three-dimensional periodic array of multi-Taub-NUT centers, containing not only centers with a positive NUT charge but also ones with a negative NUT charge. The latter are regarded as representing the asymptotic form of the Atiyah-Hitchin metric. The periodic arrays of Taub-NUT centers have close parallels with ionic crystals, where the Gibbons-Hawking potential plays the role of the Coulomb static potential of the ions, and are similarly classified according to their space groups. After a periodic identification and a Z2 projection, the array is tr…
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.
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 …
This article focuses on the new approach to the nature of a nut parameter $n$, usually treated as a dual charge to the mass. Instead of thinking about it as a gravitational analog of the magnetic monopole, we will show that the Taub-NUT spacetime conceals a peculiar rotation coming from the Misner strings depending on the nut value. Besides reconciling a number of confusing results present in the literature, this allows us to establish a consistent description of the black hole thermodynamics for the Lorentzian Taub--NUT spacetime with essential contribution from the Misner strings to the angu…
We study M5 branes on $\mathbb{R}^{1,1} \times$Taub-NUT that we view as a singular fibration. Reducing the M5 branes along the fiber gives 5d SYM. Due to the singularity, this 5d theory has a gauge anomaly and it is not supersymmetric. To cure these problems we add a supersymmetric gauged chiral WZW theory on the 2d submanifold where the circle fiber vanishes. In addition we add a mass term for the five scalar fields located on this submanifold. With all this, we obtain a fully supersymmetric and gauge invariant theory.
The Geodesic Motion in Taub-Nut Spinning Space
本文分析了自旋粒子在欧氏Taub-NUT空间中的测地线运动。本文研究了自旋空间的广义Killing方程，并根据这些方程的解导出了运动常数。一个简单的精确的解决方案，相应的轨迹躺在一个圆锥，给出。
We wish to construct solutions of Taub-NUT spacetime in Einstein-Born-Infeld gravity in even dimensions. Since Born-Infeld theory is a nonlinear electrodynamics theory, in leads to nonlinear differential equations. However a proper analytical solution was not obtain, we try to solve it numerically (by the Runge-Kotta method) with initial conditions coinciding with those of our previous work in Einstein-Maxwell gravity. We solve equations for 4, 6 and 8 dimensions and do data fitting by the least-squares method. For N=l=b=1, the metric turns to the NUT solution only in 8 dimensions, but in 4 an…
We use the recently-constructed explicit duality transformation that relates a rotating anti-D6-D4-D2-D0 black hole solution to a rotating M5-M2-P black string to construct a non-supersymmetric black ring in Taub-NUT that has two angular momenta, as well as M2 charges and M5 dipole moments. This is the first black ring solution that has both dipole charges and rotation along the S^2 of the horizon, and hence can be thought of as the "Pomeransky-Senkov" version of the M5-M2 black ring in Taub-NUT. Its physics should provide a testing ground for the applicability of the blackfold approach to cha…
The destruction of a regular black hole event horizon might provide us the possibility to access regions inside black hole event horizon. This paper investigates the possibility of overcharging a charged Taub-NUT regular black hole via the scattering of a charged field and the absorption of a charged particle. For the charged scalar field scattering, both the near-extremal and extremal charged Taub-NUT regular black holes cannot be overcharged. For the test charged particle absorption, the result shows that the event horizon of the extremal charged Taub-NUT regular black hole still exists whil…
We present details of the harmonic space construction of a quaternionic extension of the four-dimensional Taub-NUT metric. As the main merit of the harmonic space approach, the metric is obtained in an explicit form following a generic set of rules. It exhibits $SU(2)\times U(1)$ isometry group and depends on two parameters, Taub-NUT `mass' and the cosmological constant. We consider several limiting cases of interest which correspond to special choices of the involved parameters.
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.
The common assertion that the Ricci flows of Einstein spaces with cosmological constant can be modelled by certain classes of nonholonomic frame, metric and linear connection deformations resulting in nonhomogeneous Einstein spaces is examined in the light of the role played by topological three dimensional (3D) Taub-NUT-AdS/dS spacetimes.
The boosted Taub-NUT metric with zero ADM mass is shown to possess a dual momentum in the direction of the boost giving credit to the existence of another 4-vector K_μin linearized gravity associated to the NUT charge and dual to the usual P_μ. Taking the infinite boost limit we obtain a shock pp-wave with NUT charge. We show that the latter is the gravitational dual of the infinitely boosted Schwarzschild metric, also known as the Aichelburg-Sexl pp-wave. We review the fact that this new shock pp-wave is also an half-BPS solution of N=1 supergravity. It has a BPS bound equal to K_t=|K_z|.
A necessary condition that a Stäckel-Killing tensor of valence 2 be the contracted product of a Killing-Yano tensor of valence 2 with itself is re-derived for a Riemannian manifold. This condition is applied to the generalized Euclidean Taub-NUT metrics which admit a Kepler type symmetry. It is shown that in general the Stäckel-Killing tensors involved in the Runge-Lenz vector cannot be expressed as a product of Killing-Yano tensors. The only exception is the original Taub-NUT metric.
Fermions in D=4 self-dual Euclidean Taub-NUT space are investigated. Dirac-type operators involving Killing-Yano tensors of the Taub-NUT geometry are explicitly given showing that they anticommute with the standard Dirac operator and commute with the Hamiltonian as it is expected. They are connected with the hidden symmetries of the space allowing the construction of a conserved vector operator analogous to the Runge-Lenz vector of the Kepler problem. This operator is written down pointing out its algebraic properties.
We present a menagerie of solutions to the vacuum Einstein equations in six, eight and ten dimensions. These solutions describe spacetimes which are either locally asymptotically adS or locally asymptotically flat, and which have non-trivial topology. We discuss the global structure of these solutions, and their relevance within the context of M-theory.
We present the complete set of analytical solutions of the geodesic equation in Taub-NUT space-times in terms of the Weierstrass elliptic function. We systematically study the underlying polynomials and characterize the motion of test particles by its zeros. Since the presence of the "Misner string" in the Taub-NUT metric has led to different interpretations, we consider these in terms of the geodesics of the space-time. In particular, we address the geodesic incompleteness at the horizons discussed by Misner and Taub, and the analytic extension of Miller, Kruskal and Godfrey, and compare with…
The Schrödinger equation is investigated in the Euclidean Taub-NUT geometry. The bound states are degenerate and an extra degeneracy is due to the conserved Runge-Lenz vector. The existence of the extra conserved quantities, quadratic in four-velocities implies the possibility of separating variables in two different coordinate systems. The eigenvalues and the eigenvectors are given in both cases in explicit, closed form.
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.
Hidden symmetries of generalized Kaluza-Klein-type metrics are studied using van Holten's systematic analysis \cite{vH} based on Killing tensors. Applied to generalized Taub-NUT metrics, Kepler-type symmetries with associated Runge-Lenz-type conserved quantities are constructed. In the multicenter case, the subclass of two-center metrics gives rise to a conserved Runge-Lenz-type scalar, while no Kepler-type constant of the motion does exist for non aligned $(N\geq3)$-centers. We also investigated the diatomic molecule system of Wilczek et al. where "truly" non-Abelian gauge fields mimicking mo…
Memory effect from the scattering of Taub-NUT black holes
利用散射振幅的软行为计算Kerr-Taub-NUT黑洞散射波形的记忆效应，发现NUT电荷在引力软动力学中引入电磁单极子所没有的新特征。
As a concrete application of the holographic correspondence to manifolds which are only asymptotically Anti-de Sitter, we take a closer look at the quaternionic Taub-NUT space. This is a four dimensional, non-compact, inhomogeneous, riemannian manifold with the interesting property of smoothly interpolating between two symmetric spaces, AdS_4 itself and the coset SU(2,1)/U(2). Even more interesting is the fact that the scalar curvature of the induced conformal structure at the boundary (corresponding to a squashed three-sphere) changes sign as we interpolate between these two limiting cases. U…
Writing the metric of an asymptotically flat spacetime in Bondi coordinates provides an elegant way of formulating the Einstein equation as a characteristic value problem. In this setting, we find that a specific class of asymptotically flat spacetimes, including stationary solutions, contains a Maxwell gauge field as free data. Choosing this gauge field to correspond to the Dirac monopole, we derive the Taub-NUT solution in Bondi coordinates.
We review the geodesic motion of pseudo-classical spinning particles in curved spaces. Investigating the generalized Killing equations for spinning spaces, we express the constants of motion in terms of Killing-Yano tensors. The general results are applied to the case of the four-dimensional Euclidean Taub-NUT spinning space. A simple exact solution, corresponding to trajectories lying on a cone, is given.
Taub--NUT Dyons in Heterotic String Theory
本文从爱因斯坦方程的Taub-NUT解出发，结合常数介子，利用$O(1,1)$变换，构造了具有非平凡介子、轴子和$U(1)$规范场的低能杂化弦论的Taub-NUT解.利用$SL(2,\rline)$变换构造了该解的电磁对偶。通过适当改变尺度变量，对偶解的极值极限对应于先前提出的精确共形场论的低能量极限。
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 compute the axial anomaly for the Taub-NUT metric on $R^4$. We show that the axial anomaly for the generalized Taub-NUT metrics introduced by Iwai and Katayama is finite, although the Dirac operator is not Fredholm. We show that the essential spectrum of the Dirac operator is the whole real line.
Thermodynamics of Taub-NUT-AdS Spactimes
本文应用广义Komar方法推导Taub-NUT-AdS时空的总质量与NUT荷，验证第一定律和Smarr关系，并推广至带电AdS NUTy时空，获得全部热力学量。
Microstates of colinear black holes embedded in a multi-center Taub-NUT spacetime are sought in 4 dimensions. A set of coupled ordinary partial differential equations are obtained and solved for almost-BPS states, where some supersymmetry is preserved in the context of N=2 supergravity in 4 dimensions. The regularity of solutions is being carefully considered and we ensure that no CTC (closed time-like curves) are present. The larger framework is that of 11-dimensional N=2 supergravity and the current theory is obtained by compactifying down to 4 dimensions.
Starting from the generic harmonic superspace action of the quaternion-Kähler sigma models and using the quotient approach we present, in an explicit form, a quaternion-Kähler extension of the double Taub-NUT metric. It possesses $U(1)\times U(1)$ isometry and supplies a new example of non-homogeneous Einstein metric with self-dual Weyl tensor.
We construct new charged solutions of the Einstein-Maxwell field equations with cosmological constant. These solutions describe the nut-charged generalisation of the higher dimensional Reissner-Nordström spacetimes. For a negative cosmological constant these solutions are the charged generalizations of the topological nut-charged black hole solutions in higher dimensions. Finally, we discuss the global structure of such solutions and possible applications.
Using the extended forms of the Heisenberg uncertainty principle from string theory and the quantum gravity theory, we drived Hawking temperature of a Taub-Nut-(A)dS black hole. In spite of their distinctive natures such as asymptotically locally flat and breakdown of the area theorem of the horizon for the black holes, we show that the corrections to Hawking temperature by the generalized versions of the the Heisenberg uncertainty principle increases like the Schwarzschild-(A)dS black hole and give the reason why the Taub-Nut-(A)dS metric may have AdS/CFT dual picture.
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