Guillaume Bossard, Hermann Nicolai, K. S. Stelle
Generalising expressions given by Komar, we give precise definitions of gravitational mass and solitonic NUT charge and we apply these to the description of a class of Minkowski-signature multi-Taub-NUT solutions without rod singularities. A Wick rotation then yields the corresponding class of Euclidean-signature gravitational multi-instantons.
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A note on the calculation of the Komar integral in the Lorentzian Taub-NUT spacetime
本文澄清 Lorentzian Taub-NUT 时空中 Komar 积分的计算，指出即使经 Misner 程序消除弦奇点，类空超曲面上仍不可避免存在 Misner 弦，因此可得到一致热力学结果。
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。
The Komar charge in presence of the Holst term and the gravitational Witten effect
本文在一阶形式中研究了引入 Holst 项对 Komar 荷的影响，发现该修正会通过 NUT 荷 $N$ 和 Barbero 参数 $α$ 改变无穷远处的 Komar 积分，从而产生类似 Witten 效应的非零质量 $αN$。
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…
Taub-NUT as gravitational dyon with torsion
研究Taub-NUT度规，发现其列维-奇维塔联络在米斯纳弦上奇异，引入挠率可改善，挠率产生Komar流并决定渐近Komar荷，最终Taub-NUT度规表现为受两束自旋流体支撑的孤子。
We compute the \emph{surface energy~(${\cal E}_{s}^{\pm}$), the rotational energy~(${\cal E}_{r}^{\pm}$) and the electromagnetic energy~(${\cal E}_{em}^{\pm}$)} for Newman-Unti-Tamburino~(NUT) class of black hole having the event horizon~(${\cal H}^{+}$) and the Cauchy horizon~(${\cal H}^{-}$). Remarkably, we find that the \emph{mass parameter can be expressed as sum of three energies i. e. $M={\cal E}_{s}^{\pm}+{\cal E}_{r}^{\pm}+{\cal E}_{em}^{\pm}$}. It has been \emph{tested} for Taub-NUT black hole, Reissner-Nordström-Taub-NUT black hole, Kerr-Taub-NUT black hole and Kerr-Newman-Taub-NUT b…
As shown recently (arXiv:1903.08668), consistent thermodynamics of the Lorentzian Taub-NUT solutions with Misner strings present can be formulated provided a new pair of conjugate quantities (related to the NUT parameter) $ψ-N$ is introduced. In (arXiv:1903.08668) this pair was calculated from the Euclidean action but no geometrical interpretation for the new quantities was provided. In this paper we propose that the potential $ψ$ should be identified with the surface gravity of the Misner string and the conjugate Misner charge $N$ can be obtained by a Komar-type integration over the tubes sur…
The dual Komar mass generalizes the concept of the NUT parameter and is akin to the magnetic charge in electrodynamics. In asymptotically flat spacetimes it coincides with the dual supertranslation charge. The dual mass vanishes identically on Riemannian manifolds in General Relativity unless conical singularities corresponding to Misner strings are introduced. In this paper we propose an alternative way to source the dual mass locally. We show that this can be done by enlarging the phase space of the theory to allow for a violation of the algebraic Bianchi identity using local fields. A minim…
Derivation of the Smarr formula from the Komar charge in Einstein-nonlinear electrodynamics theories and applications to regular black holes
通过将耦合常数提升为动力学场，构造广义Komar荷，推导出包含耦合常数贡献的Smarr公式，并应用于规则Bardeen黑洞的热力学分析。
Generalized Komar charges and Smarr formulas for black holes and boson stars
本文推广了Komar荷使其在含物质时在壳闭合以构建Smarr公式，并利用该荷及其他闭合形式荷证明引力孤子与玻色子星的不存在定理，同时展示广义对称假设如何规避这些定理。
We investigate the thermodynamical properties of solutions to the 5D Einstein and Einstein-Maxwell-dilaton equations describing static black holes on ALF gravitational instantons. Some general expressions regarding the nut charge and potential are derived, as well as Smarr-like relations. The thermodynamics of two particular solutions representing a static black hole on Taub-Nut and Taub-Bolt instantons are examined in detail. Two dierent approaches for computation of the mass and the tension - the Komar and counterterm method, are applied and compared. A new charged black hole on Taub-Bolt in…
We compute area (or entropy) product formula for Newman-Unti-Tamburino (NUT) class of black holes. Specifically, we derive the area product of outer horizon and inner horizon (${ \mathcal{H}}^{\pm }$) for Taub-NUT, Euclidean Taub-NUT black hole, Reissner-Nordström--Taub-NUT black hole, Kerr-Taub-NUT black hole and Kerr-Newman-Taub-NUT black hole under the formalism developed very recently by Wu et al. \cite{wu} [PRD 100, 101501(R) (2019)]. The formalism is that a generic four dimensional Taub-NUT spacetime should be described completely in terms of three or four different types of thermodynami…
It is well known that, for even n, the n-soliton solution on the Minkowski seed, constructed using the inverse-scattering method (ISM) of Belinski and Zakharov (BZ), is the multi-Kerr-NUT solution. We show that, for odd n, the natural seed to use is the Euclidean space with two manifest translational symmetries, and the n-soliton solution is the accelerating multi-Kerr-NUT solution. We thus define the n-soliton solution on flat space for any positive integer n. It admits both Lorentzian and Euclidean sections. In the latter section, we find that a number, say m, of solitons can be eliminated i…
In our previous work, a novel idea that the NUT charge can be thought of as a thermodynamical multi-hair has been advocated to describe perfectly the thermodynamical character of the generic four-dimensional Taub-NUT spacetimes. According to this scheme, the Komar mass M, the gravito-magnetic charge and/or the dual (magnetic) mass N, together with a new secondary hair J_N=MN, namely, a Kerr-like conserved angular momentum, enter into the standard forms of the first law and Bekenstein-Smarr mass formula. Distinguished from other recent attempts, our consistent thermodynamic differential and int…
We apply a new general method of anholonomic frames with associated nonlinear connection structure to construct new classes of exact solutions of Einstein-Dirac equations in five dimensional (5D)gravity. Such solutions are parametrized by off-diagonal metrics in coordinate (holonomic) bases, or, equivalently, by diagonal metrics given with respect to some anholonomic frames (pentads, or funfbiends, satisfing corresponding constraint relations). We consider two possibilities of generalization of the Taub NUT metric in order to obtain vacuum solutions of 5D Einsitein equations with effective ren…
Thermodynamics of Taub-NUT and Plebanski Solutions
本文通过类比视界零 Killing 向量与极点退化 Killing 向量，建立 NUT 荷与 Misner 弦的热力学描述，并用 Wald、Euclidean 作用量和 Komar 方法验证其一致性。
We first reconstruct the conserved (Abbott-Deser) charges in the spin connection formalism of gravity for asymptotically (Anti)-de Sitter spaces, and then compute the masses of the AdS soliton and the recently found Eguchi-Hanson solitons in generic odd dimensions, unlike the previous result obtained for only five dimensions. These solutions have negative masses compared to the global AdS or AdS/Z_p spacetimes. As a separate note, we also compute the masses of the recent even dimensional Taub-NUT-Reissner-Nordstrom metrics.
Entropy Product Function and Central charges in NUT Geometry
本文为TNUT黑洞定义熵积函数(EPF)，通过Cardy公式推导对偶CFT的中心荷，发现中心荷与EPF的偏导关系，并利用Bézout恒等式生成更多全息描述，最后将该中心荷推导扩展至RNNUT、KNUT和KNNUT黑洞。
It is demonstrated that the generic four-dimensional Taub-Newman-Unti-Tamburino (Taub-NUT) spacetimes can be perfectly described in terms of three or four different kinds of thermodynamic hairs: the Komar mass ($M = m$), the "angular momentum" ($J_n = mn$), the gravitomagnetic charge ($N = n$), and/or the dual (magnetic) mass ($\widetilde{M} = n$). In other words, the NUT charge is a thermodynamic multihair which means that it simultaneously has both rotation-like and electromagnetic charge-like characteristics; this is in sharp contrast with the previous knowledge that it has only one physica…
Bekenstein-Hawking Entropy Products for NUT class of Black Holes in AdS Space
本文推导了Taub-NUT-de Sitter和Taub-NUT-anti-de Sitter黑洞的与质量无关的熵积规则，并基于新形式揭示了其普适性源于与Kerr类角动量相似的新守恒荷J_{N}=MN。
In this paper we show how two dimensional electron systems can be modeled by strings interacting with D-branes. The dualities of string theory allow several descriptions of the system. These include descriptions in terms of solitons in the near horizon D6-brane theory, non-commutative gauge theory on a D2-brane, the Matrix Theory of D0-branes and finally as a giant graviton in M-theory. The soliton can be described as a D2-brane with an incompressible fluid of D0-branes and charged string-ends moving on it. Including an NS5 brane in the system allows for the existence of an edge with the chara…
We discuss some aspects of higher-dimensional gravitational solitons and kinks, including in particular their stability. We illustrate our discussion with the examples of (non-BPS) higher-dimensional Taub-NUT solutions as the spatial metrics in (6+1) and (8+1) dimensions. We find them to be stable against small but non-infinitesimal disturbances, but unstable against large ones, which can lead to black-hole formation. In (8+1) dimensions we find a continuous non-BPS family of asymptotically-conical solitons connecting a previously-known kink metric with the supersymmetric A_8 solution which ha…
We construct the first analytic self-gravitating Skyrmions with higher Baryon charge in four dimensions for the $SU(3)$-Skyrme-Einstein-$Λ$ theory by combining the generalized hedgehog ansatz with the approach developed by Balachandran et al. to describe the first (numerical) example of a non-embedded solution. These are genuine $SU(3)$ analytic solutions instead of trivial embeddings of $SU(2)$ into $SU(3)$ and its geometry is that of a Bianchi IX Universe. The Skyrme ansatz is chosen in such a way that the Skyrme field equations are identically satisfied in the sector with Baryon charge 4. T…
The antisoliton-soliton {\cal G}={\cal S_-}\!\vee{\cal S_+} neutral state is a proper geon in a family of stable squashed-S^3\times\IR pp-wave electrovacua along a primordial Q/r^2 field. With {\cal S_-} propagating backwards in time, the dominant EM field is that of an effective electric-dipole moment {\sf p}. If disjointed, the {\cal S_\pm} carry \pm Q charge (on a round-S^2 {\em physical} singularity of radius r_o) as non-singular alternatives to the Kerr-Newman solution. {\cal G} has three scales (gravitational κ, metric scale, NUT-charge κQ=2r_o) in a full 4-scale hierarchy without supers…
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