Finite BMS transformations
Glenn Barnich, Cédric Troessaert
在三维和四维情形下，计算了有限BMS和Weyl变换对零无穷远点引力数据的作用，给出了Scri上边界度规的任意共形因子。
The action of finite BMS and Weyl transformations on the gravitational data at null infinity is worked out in three and four dimensions in the case of an arbitrary conformal factor for the boundary metric induced on Scri.
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Fully nonlinear transformations of the Weyl-Bondi-Metzner-Sachs asymptotic symmetry group
本文计算了Weyl-BMS渐近对称群的完全非线性变换对Bondi规范度规函数的作用，推广了先前线性化及BMS背景下的非线性结果，为探索BMSW群的含义提供了工具。
From parabolic to loxodromic BMS transformations
Bondi-Metzner-Sachs（BMS）变换中有一半是由扩展复平面的保向共形同胚组成的，称为分数线性（或Mobius）变换。这些可以是4种，即它们被分类为抛物线，或双曲线，或椭圆，或斜航，取决于固定点的数量和SL（2，C）群的投影版本中相关的2x2矩阵的迹的值。由此产生的SL（2，C）矩阵的特殊形式也影响BMS变换的另一半，并且在这里被用来提出我们再次称为抛物线、双曲、椭圆或斜驶的渐近对称群的4种实现。本文的第二部分证明了迹趋于无穷大的双曲变换和斜驶变换的子集对应于奇异Sturm-Liouville问题极限点条件的满足。因此，在描述渐近平坦时空的语言和复分析世界以及普通量子力学中的自伴问题之间可能存在着深刻的联系。
When two spacetimes are stitched across a null-shell placed at the horizon of a black hole BMS-supertranslation like soldering freedom arises if one demands the induced metric on the horizon shell should remain invariant under the translations generated by the null generators of the shell. We revisit this phenomenon at the horizon of rotating shells and obtain BMS like symmetries. We further show that superrotation like soldering symmetries in the form of conformal isometries can emerge whenever the degenerate metric of any null hypersurface admits a dependency on null (degenerate direction) c…
We define and study asymptotic Killing and conformal Killing vectors in $d$-dimensional Minkowski, (A)dS, $\mathbb{R}\times S^{d-1}$ and ${\rm AdS}_2\times S^{d-2}$. We construct the associated quantum charges for an arbitrary CFT and show they satisfy a closed algebra that includes the BMS as a sub-algebra (i.e. supertranslations and superrotations) plus a novel transformation we call `superdilations'. We study representations of this algebra in the Hilbert space of the CFT, as well as the action of the finite transformations obtained by exponentiating the charges. In the context of the AdS/C…
Horizon Shells and BMS-like Soldering Transformations
我们重温了广义相对论中的零壳理论，特别强调放置在黑洞视界的零壳。我们详细研究了相当大的自由度，可在这种情况下，一个焊接两个度量一起跨越零超曲面（如杀死地平线）的诱导度量是不变的平移下沿零发电机。在这种情况下，焊接变换群是无限维的，这些焊接产生了包含无质量物质和脉冲引力波分量的非平凡视界壳。我们也用卡罗对称群的语言重新表述了这个结果。为了说明这一现象，我们详细讨论的例子壳的视界上的史瓦西黑洞（具有相等的内部和外部质量），揭示了丰富的经典结构的视界，并推导出一个明确的表达一般视界壳能量动量张量。在特殊情况下的BMS焊接超平移，我们发现一个保守的壳能量是惊人的相似的渐近BMS超平移收费的标准表达式，这表明这些视界壳的物理性质和最近提出的BMS超平移头发的黑洞之间的直接关系。
On BMS Invariance of Gravitational Scattering
BMS+变换作用于传出的引力散射数据，同时保持内在结构在未来的零无限（I+）。BMS-转换类似地作用于过去零无穷大（I-）的输入数据。在本文中，我们应用-在一个适当的有限邻域的闵可夫斯基真空-结果的Christodoulou和Klainerman连接I+到I-，从而确定“对角”元素BMS 0（BMS+）X（BMS-）。我们认为BMS 0是经典引力散射和量子引力S-矩阵的非平凡无穷维对称。它意味着I+处的共形S2上每个角度的净累积能流守恒。相关的沃德恒等式示出与S-矩阵元素与软引力子和没有。最后，我们将BMS 0转化为U（1）Kac-Moody对称，并给出了Kac-Moody流在零无穷远边界上的一个软引力子算符的表达式.
On the nature of Bondi-Metzner-Sachs transformations
本文系统分析 BMS 变换的椭圆、抛物、双曲和斜驶四族，证明正规椭圆变换对应超平移，刻画共形因子单调性与 Killing 向量场，并通过齐次坐标和 Segre 流形揭示其为一般变换在单位圆上的限制。
Starting from gravity in asymptotically flat spacetime, the BMS momentum fluxes are constructed. These are non-local expressions of the solution space living on the celestial Riemann surface. They transform in the coadjoint representation of the extended BMS group and correspond to Virasoro primaries under the action of bulk superrotations. The relation between the BMS momentum fluxes and celestial CFT operators is then established: the supermomentum flux is related to the supertranslation operator and the super angular momentum flux is linked to the stress-energy tensor of the celestial CFT. …
Aspects of the BMS/CFT correspondence
在回顾了AdS 3/CFT 2对应中涉及的对称性和经典解之后，我们对3维和4维的零无穷大渐近平坦时空进行了类似的分析。在二维共形场论的精神下，四维零无穷远处渐近平坦时空的对称代数被视为具有无穷小局部共形变换的超平移的半直和，而不是像通常那样，具有洛伦兹代数。作为第一个应用，我们推导出如何对称代数实现的解决方案空间。特别地，我们计算了Bondi的新闻张量、质量和角动量在局部共形变换下的行为。
The present thesis aims at providing a unified description of radiative phase spaces in General Relativity for any value of the cosmological constant using covariant phase space methods. We start by considering generic asymptotically locally (A)dS spacetimes with leaky boundary conditions in the Starobinsky/Fefferman-Graham gauge. The boundary structure is allowed to fluctuate and plays the role of source yielding some flux of gravitational radiation at the boundary. The holographic renormalization procedure is employed to obtain finite surface charges for the whole class of boundary diffeomor…
Transformation of mass-angular momentum aspect under BMS transformations
该研究通过曲率张量提取和度规系数提取两种方法，推导得到BMS变换下质量与角动量荷面的确定性变换公式，验证了Dray-Streubel角动量相关关系，给出一般截面该角动量的精确表达式，解决了文献中的相关不一致问题。
The Poisson brackets of the gravitational field at null infinity play a pivotal role in establishing the equivalence between the Ward identities involving BMS charges and the soft graviton theorem. In recent literature it was noticed that, in order to reproduce the action of BMS transformations via such Poisson brackets, one needs to add "ad-hoc" boundary terms in the symplectic form. In this note we show that, introducing a suitable splitting of the gravitational field in bulk and boundary degrees of freedom and using techniques of covariant phase space formalism, it is possible to obtain the…
It has been argued that the symmetries of gravity at null infinity should include a Diff$(S^2)$ factor associated to diffeomorphisms on the celestial sphere. However, the standard phase space of gravity does not support the action of such transformations. Building on earlier work by Laddha and one of the authors, we present an extension of the phase space of gravity at null infinity on which Diff$(S^2)$ acts canonically. The Poisson brackets of supertranslation and Diff$(S^2)$ charges reproduce the generalized BMS algebra introduced in arXiv:1408.2228 .
Starting from an action principle adapted to the Newman-Penrose formalism, we provide a self-contained derivation of BMS current algebra, which includes the generalization of the Bondi mass loss formula to all BMS generators. In the spirit of the Newman-Penrose approach, infinitesimal diffeomorphisms are expressed in terms of four scalars rather than a vector field. In this framework, the on-shell closed co-dimension two forms of the linearized theory associated with Killing vectors of the background are constructed from a standard algorithm. The explicit expression for the breaking that occur…
BMS in Cosmology
对称性在宇宙学中扮演着一个有趣的角色。它们在描述暴胀过程中产生的宇宙学扰动方面是有用的，并导致涉及大尺度结构暗物质和星系超密度统计因子软极限的一致性关系。另一方面，在观测宇宙学中，这些大尺度统计分布信息的载体是在零测地线上传播的光线。出于这个简单的考虑，我们研究了零无穷大的结构和相关的BMS对称性的宇宙学设置。对于减速Friedmann-Robertson-Walker背景，未来零无穷大的存在，我们发现BMS变换，离开渐近度量不变的领先秩序。与渐近平坦的情况相反，宇宙学中的BMS变换产生对应于标量和张量自由度的Goldstone模，这些自由度可能存在于零无穷大并扰动渐近数据。因此，BMS变换产生物理上不等价的真空，因为它们用这些物理自由度填充了零无穷大的宇宙。我们还讨论了考虑宇宙膨胀时的引力记忆效应。在这种情况下，由于滞后格林函数的尾部对引力记忆有额外的贡献，它不仅在光锥上得到支持，而且在光锥内部也得到支持。引力记忆效应也可以从渐近的观点理解为宇宙学BMS相关真空之间的过渡。
We show that we can combine the (complex, self-dual) BMS vector fields with the recently defined BMS twistors to obtain a new supersymmetric extension of the BMS symmetries at null infinity. We compare our construction to other supersymmetric extensions of the BMS algebra proposed in the context of supergravity. Unlike the standard constructions the anticommutator in our superalgebra generates all the BMS vector fields including the Lorentz transformations. We also show that there exists a projection from our BMS Lie superalgebra to the global subalgebra of the Neveu-Schwarz supersymmetries on…
Supertranslations are Soft Dressings
本文在KMOC形式体系下，研究大规范/BMS变换对粒子态修饰的经典含义，通过多类理论阐明软因子化驱动的构造，揭示大规范变换对两粒子态的影响及相关框架效应。
Cataclysmic astrophysical phenomena can produce impulsive gravitational waves that can possibly be detected by the advanced versions of present-day detectors in the future. Gluing of two spacetimes across a null surface produces impulsive gravitational waves (in the phraseology of Penrose [1]) having a Dirac Delta function type pulse profile along the surface. It is known that BMS-like symmetries appear as soldering freedom while we glue two spacetimes along a null surface. In this note, we study the effect of such impulsive gravitational waves on test particles (detectors) or geodesics. We sh…
A geometrical invitation to BMS group theory
本文通过几何方法介绍BMS群理论，探讨其在任意维度中的定义、结构及与Minkowski时空的关系。
Constraints on BMS Transformations via Energy Conditions and implications on black hole geometry
通过能量条件约束BMS变换，发现SEC和WEC在次主导阶对超翻译函数施加角限制，而NEC和DEC在NNLO阶出现最强约束，限制了可接受的超翻译空间。
Modeling the BMS transformation induced by a binary black hole merger
本文构建了双黑洞并合引起的BMS变换模型，利用高斯过程回归拟合数值相对论模拟数据，首次提供超平移模型，并发现特征演化波形预测的反冲速度比外推波形约大5%。
The conformal symmetry algebra in 2D (Diff($S^{1}$)$\oplus$Diff($S^{1}$)) is shown to be related to its ultra/non-relativistic version (BMS$_{3}$$\approx$GCA$_{2}$) through a nonlinear map of the generators, without any sort of limiting process. For a generic classical CFT$_{2}$, the BMS$_{3}$ generators then emerge as composites built out from the chiral (holomorphic) components of the stress-energy tensor, $T$ and $\bar{T}$, closing in the Poisson brackets at equal time slices. Nevertheless, supertranslation generators do not span Noetherian symmetries. BMS$_{3}$ becomes a bona fide symmetry…
Transformations of asymptotic gravitational-wave data
引力波数据是规范相关的。虽然我们可以限制这类数据可以表达的仪表类，但仍然允许有无限维的变换组，同时保留在这类中，并且几乎有尽可能多的不同--尽管物理上等效--波形。本文提出了一种计算最重要的变换群Bondi-Metzner-Sachs（BMS）群的影响的方法，该群由旋转、提升和超平移（包括时间和空间平移作为特例）组成。为了合理的近似，这些变换导致在波形的自旋加权球谐分解中的模式之间的简单耦合。结果表明，从公开的SXS波形目录中的模拟紧凑型二进制的波形包含未建模的影响，由于位移和漂移的质心，占模式混合在1%的典型水平。然而，这些影响可以通过测量系统的质心对于一部分内旋的平均运动，并对波形数据应用相反的变换来减轻。更一般地说，控制BMS变换对于消除数值波形和分析波形的引力波数据中固有的规范模糊性是必要的。实现波形BMS转换的开源代码与本文一起包含在补充材料中。
Representations of the ultrahyperbolic BMS group HB. III. Determination of the representations induced from finite little groups
普通的Bondi-Metzner-Sachs（BMS）群B是所有渐近平坦洛伦兹时空的公共渐近对称群。因此，B是广义相对论的普适对称群的最佳候选者。然而，在研究量子引力时，经常会考虑具有不同于通常洛伦兹特征的时空和复杂时空。前面已经定义了适合于这些其他签名的B的推广。特别地，HB是BMS组的适合于超双曲线签名（+，+，-，-）的变体，已在以前的文章中定义，其中表明HB的所有强连续酉不可约表示（IR）可以用Wigner-Mackey的诱导方法，并且HB的所有子群都是紧的.这里我们详细地描述了HB的所有有限子群，并且我们发现HB的所有子群都是紧的诱导HB的IR。
Accurate models of gravitational waves from merging binary black holes are crucial for detectors to measure events and extract new science. One important feature that is currently missing from the Simulating eXtreme Spacetimes (SXS) Collaboration's catalog of waveforms for merging black holes, and other waveform catalogs, is the gravitational memory effect: a persistent, physical change to spacetime that is induced by the passage of transient radiation. We find, however, that by exploiting the Bondi-Metzner-Sachs (BMS) balance laws, which come from the extended BMS transformations, we can corr…
Hamiltonian structure and asymptotic symmetries of the Einstein-Maxwell system at spatial infinity
我们提出了一套新的渐近条件，重力在空间无穷远，其中包括重力磁型的解决方案，允许一个非平凡的哈密顿行动的完整的$BMS_4$代数，并导致非发散行为的Weyl张量作为一个接近零无穷大。然后，我们扩展到耦合Einstein-Maxwell系统的分析，并获得作为规范实现的渐近对称代数的半直和的$BMS_4$代数与角度相关的$u(1)$变换。与每个渐近对称元素相关联的哈密顿电荷生成元被明确地写出。还讨论了在零无穷远处与匹配条件的关系。
Gravitational vacua in the Newman-Penrose formalism
本文在Newman-Unti规范下求解了曲率张量消失的Newman-Penrose方程，得到引力真空解，并证明其超平移荷在含Holst、Pontryagin和Gauss-Bonnet项时仍严格为零。
Phase Space Renormalization and Finite BMS Charges in Six Dimensions
本文系统分析了六维 Einstein 引力解空间，提出相空间重整化技术，利用局部协变抵消项重整化辛势，证明 GBMS 荷可积部分忠实表示 GBMS 代数，解决了高维偶数非线性引力中无限维渐近对称性存在的长期问题，并揭示软引力子定理等价于 Ward 恒等式。
Vacua of the gravitational field
庞加莱不变真空在量子引力中不是唯一的。BMS超平移对称性最初定义在零无穷远自发破缺，并导致不等价的庞加莱真空。本文构造了唯一的真空，它插在BMS规范的过去和未来零无限之间，完全由定义在球上的打破BMS不变性的任意Goldstone玻色子来刻画。我们表明，这些真空包含一个缺陷，不携带庞加莱费用，但一般携带超旋转费用。我们认为，有一个巨大的退化真空多缺陷。我们还提出了单缺陷真空及其正则共轭源，它可以从一个刘维尔玻色子在球极投影平面上构造。我们表明，积极的能量迫使玻色子的应力张量消失的边界条件。因此，开启源的有限超旋转在物理上被排除为真空周围的正则变换。然而，无穷小超旋转是外部辛对称，与描述Goldstone玻色子的守恒电荷有关。
Infrared finite scattering theory: Scattering states and representations of the BMS group
针对无质量场散射的红外发散问题，本文通过记忆的 Lorentz 轨道直积表示构造有限能量、角动量的物理态，并给出 BMS 荷作用。
We present a new gauge for asymptotically flat spacetime that can treat future and past null infinities ($\mathscr{I}^{+}$ or $\mathscr{I}^{-}$) democratically. Our gauge is complementary to Bondi and Ashtekar-Hansen gauges, and is adapted to the $S$-matrix being the natural observable. One new feature is that the holographic directions are null. We present a set of consistent fall-offs in terms of null coordinates at $\mathscr{I}^{+}$ and $\mathscr{I}^{-}$, with finite BMS$^{\pm}$ charges. The diagonal BMS$^0$ symmetry of the gravitational $S$-matrix emerges upon demanding {\em asymptotic} CP…
Gravitational Black Hole Hair from Event Horizon Supertranslations
我们讨论BMS超平移零无限和视界的情况下的史瓦西黑洞。我们表明，这两种超平移导致无限多的无隙物理激发。在此基础上，我们构造了一个商代数，使用适合的叠加这两种转换，不能补偿由一个普通的BMS超平移，因此本质上是由于存在一个事件视界。我们表明，这些商变换是物理的，并在视界上产生无隙激发，可以解释引力头发以及黑洞熵。我们确定这些模式的物理与Bogolioubov-Goldstone模式由于量子临界。传统上，这些无间隙模式的数量是无限的。然而，我们表明，由于量子临界性的信息载体的实际数量变得有限，并与贝肯斯坦熵一致。虽然我们只考虑史瓦西几何的情形，但这些论证可以推广到包含事件视界的任意时空。
We construct a map of solutions of the dispersionless BKP (dBKP) equation to solutions of the Manakov-Santini (MS) system. This map defines an Einstein-Weyl structure corresponding to the dBKP equation through the general Lorentzian Einstein-Weyl structure corresponding to the MS system. We give a spectral characterisation of reduction of the MS system which singles out the image of the dBKP equation solutions and also consider more general reductions of this class. We define the BMS system and extend the map defined above to the map (Miura transformation) of solutions of the BMS system to sol…
Supertranslations: redundancies of horizon data, and global symmetries at null infinity
本文讨论了定义在一般非膨胀视界（NEH）上的光滑超平移的几何性质。为此，我们考虑了真空爱因斯坦方程对NEH结构的约束，并讨论了它们的解在超平移下的变换性质。我们提出了一个自由指定的数据集，这是必要的和足够的重建全地平线的几何形状，是由对象是不变的超平移。我们的结论是，光滑超平移不改变NEH的几何形状，它们应该被视为纯规范。我们的结果适用于固定的，非稳态的NEH，后者能够描述辐射过程发生在地平线上。作为一致性检查，我们重复分析定义在null infinity上的BMS超平移，$\mathcal{I}$。使用与NEH相同的框架，我们恢复了众所周知的结果，即BMS超平移对$\mathcal{I}$上的自由数据起着非平凡的作用。完整的分析是在精确的、非线性的、广义相对论中进行的。
Null hypersurface quantization, electromagnetic duality and asymptotic symmetries of Maxwell theory
本文考虑在麦克斯韦理论的量子化过程中引入正则化。这允许系统地讨论各种边界条件下的非线性算子，并以受控的方式相应地应用狄拉克括号。当我们考虑像大规范变换那样不局限于边界$u\to \pm \infty$的渐近电荷时，这种方法是最有用的。我们表明，我们的方法再现算子代数在已知的情况下，它可以应用到其他时空对称收费，如BMS变换。我们还得到了U（1）电荷的渐近形式在一个显式EM对称Schwarz-Sen型作用量的电磁对偶性。使用我们的正则化方法，我们证明了电荷产生的螺旋算子的预期变换。我们的方法有望在更一般的理论应用。
Recently there are more and more interest on the gravitational wave of moving sources. This introduces a Lorentz transformation problem of gravitational wave. Although Bondi-Metzner-Sachs (BMS) theory has in principle already included the Lorentz transformation of gravitational wave, the transformation of the three dimensional gravitational wave tensor has not been explicitly calculated before. Within four dimensional spacetime, gravitational wave have property of `boost weight zero' and `spin weight 2'. This fact makes the Lorentz transformation of gravitational wave difficult to understand. …
We show that we can derive the asymptotic Einstein's equations that arises at order $1/r$ in asymptotically flat gravity purely from symmetry considerations. This is achieved by studying the transformation properties of functionals of the metric and the stress-energy tensor under the action of the Weyl BMS group, a recently introduced asymptotic symmetry group that includes arbitrary diffeomorphisms and local conformal transformations of the metric on the 2-sphere. Our derivation, which encompasses the inclusion of matter sources, leads to the identification of covariant observables that provi…
We present a foliation-focused critical review of the boundary conditions and dynamics of 4D gravitational theories. A general coordinate transformation introduces a new foliation and changes the hypersurface on which a natural boundary condition is imposed; in this sense gauge transformations must be viewed as changing the boundary conditions. The issue of a gauge invariant boundary condition is nontrivial and has been extensively studied in the literature. We turn around the difficulty in obtaining such a boundary condition (and subtleties observed in the main body) and take it as one of the…
Finite Transformations in Doubled and Exceptional Space
在双场论中，规范对称性被实现为双时空中的广义规范同态。由于理论的一致性，张量场对二重坐标的依赖性受到很强的约束。这使得有限变换定律在技术上和概念上都非常复杂。本文提出了一种新的，物理直观的方法，利用矢量场的无扭形式的有限规范变换。在我们的方法中，有限规范变换律表示在一个最大的零子空间上的动力学自由度的生活和本地旋转的这个零子空间内嵌入的双重空间的的同态。我们表明，我们的有限变换自动满足复合律。我们还证明了我们的方法不存在所谓的Papadopoulos问题，因此可以用非平凡的三形式通量$H_3$来描述背景。我们的方法的另一个优点是直接适用于一般的扩展场论。我们通过在SL（5）例外场论中得到有限变换律来证明这一点。
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