A. R. Kashif, K. Saifullah, G. Shabbir
Symmetries of geometrical and physical quantities in general relativity provide important information about the curvature structure of the spacetimes. Symmetries of the curvature and the Weyl tensors, known as curvature and Weyl collineations respectively, are two of such important symmetries. Some results on these symmetries for Bianchi type V spacetimes are discussed.
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A study of proper Weyl collineations in Kantowski-Sachs and Bianchi type III space-times is given by using the rank of the 6X6 Weyl matrix and direct integration techniques. Studying proper Weyl collineations in each of the above space-times, it is shown that there exists no such possibility when the above space-times admit proper Weyl collineations.
The purpose of this paper is to revisit the Bianchi identities existing for the Riemann and Weyl tensors in the combined framework of the formal theory of systems of partial differential equations (Spencer cohomology, differential systems, formal integrability) and Algebraic Analysis (homological algebra, differential modules, duality). In particular, we prove that the n 2 (n 2 -- 1)(n -- 2)/24 generating Bianchi identities for the Riemann tensor are first order and can be easily described by means of the Spencer cohomology of the first order Killing symbol in arbitrary dimension n $\ge$ 2. Si…
We analyse in a systematic way the (non-)compact four dimensional Einstein-Weyl spaces equipped with a Bianchi metric. We show that Einstein-Weyl structures with a Class A Bianchi metric have a conformal scalar curvature of constant sign on the manifold. Moreover, we prove that most of them are conformally Einstein or conformally Kähler ; in the non-exact Einstein-Weyl case with a Bianchi metric of the type $VII_0, VIII$ or $IX$, we show that the distance may be taken in a diagonal form and we obtain its explicit 4-parameters expression. This extends our previous analysis, limited to the diago…
We analyse in a systematic way the four dimensionnal Einstein-Weyl spaces equipped with a diagonal Kähler Bianchi IX metric. In particular, we show that the subclass of Einstein-Weyl structures with a constant conformal scalar curvature is the one with a conformally scalar flat - but not necessarily scalar flat - metric ; we exhibit its 3-parameter distance and Weyl one-form. This extends previous analysis of Pedersen, Swann and Madsen , limited to the scalar flat, antiself-dual case. We also check that, in agreement with a theorem of Derdzinski, the most general conformally Einstein metric in…
The Noether symmetry approach is useful tool to restrict the arbitrariness in a gravity theory when the equations of motion are underdetermined due to the high number of functions to be determined in the ansatz. We consider two scalar-coupled theories of gravity, one motivated by induced gravity, the other more standard; in Bianchi I, Bianchi III and Kantowski-Sachs cosmological models. For these models, we present a full set of Noether gauge symmetries, which are more general than those obtained by the strict Noether symmetry approach in our recent work. Some exact solutions are derived using…
In this work we perform the symmetry classification of the Klein Gordon equation in Bianchi I spacetime. We apply a geometric method which relates the Lie symmetries of the Klein Gordon equation with the conformal algebra of the underlying geometry. Furthermore, we prove that the Lie symmetries which follow from the conformal algebra are also and Noether symmetries for the Klein Gordon equation. We use these resutls in order to determine all the potentials in which the Klein Gordon admits Lie and Noether symmetries. Due to the large number of cases and for easy reference the results are presen…
We use our Nöther Symmetry Approach to study the Einstein equations minimally coupled with a scalar field, in the case of Bianchi universes of class A and B. Possible cases, when such symmetries exist, are found and two examples of exact integration of the equations of motion are given in the cases of Bianchi AI and BV.
We scrutinize the overall structure of the space of cosmological models of Bianchi type I-VII$_h$ that contain a free massless scalar field, with a spatially homogeneous gradient $\nabla_μφ$ that generally breaks isotropy, in addition to a standard perfect fluid. Specifically, state space is written as a union of disjoint invariant sets, each corresponding to a particular cosmological model that is classified with respect to the Bianchi type and the matter content. Subsets corresponding to higher-symmetry models, including all locally rotationally symmetric models and FLRW models, and models w…
We carried out the detailed group classification of the potential in Klein-Gordon equation in anisotropic Riemannian manifolds. Specifically, we consider the Klein-Gordon equations for the four-dimensional anisotropic and homogeneous spacetimes of Bianchi I, Bianchi\ III and Bianchi V. We derive all the closed-form expressions for the potential function where the equation admits Lie and Noether symmetries. We apply previous results which connect the Lie symmetries\ of the differential equation with the collineations of the Riemannian space which defines the Laplace operator, and we solve the c…
Lie symmetries are discussed for the Wheeler-De Witt equation in Bianchi Class A cosmologies. In particular, we consider General Relativity, minimally coupled scalar field gravity and Hybrid Gravity as paradigmatic examples of the approach. Several invariant solutions are determined and classified according to the form of the scalar field potential. The approach gives rise to a suitable method to select classical solutions and it is based on the first principle of the existence of symmetries.
We analyze carefully the problem of gauge symmetries for Bianchi models, from both the geometrical and dynamical points of view. Some of the geometrical definitions of gauge symmetries (=``homogeneity preserving diffeomorphisms'') given in the literature do not incorporate the crucial feature that local gauge transformations should be independent at each point of the manifold of the independent variables ( = time for Bianchi models), i.e, should be arbitrarily localizable ( in time). We give a geometrical definition of homogeneity preserving diffeomorphisms that does not possess this shortcomi…
All diagonal proper Bianchi I space-times are determined which admit certain important symmetries. It is shown that for Homotheties, Conformal motions and Kinematic Self-Similarities the resulting space-times are defined explicitly in terms of a set of parameters whereas Affine Collineations, Ricci Collineations and Curvature Collineations, if they are admitted, they determine the metric modulo certain algebraic conditions. In all cases the symmetry vectors are explicitly computed. The physical and the geometrical consequences of the results are discussed and a new anisitropic fluid, physicall…
We reformulate the dynamics of homogeneous cosmologies with a scalar field matter source with an arbitrary self-interaction potential in the language of jet bundles and extensions of vector fields. In this framework, the Bianchi-scalar field equations become subsets of the second Bianchi jet bundle, $J^2$, and every Bianchi cosmology is naturally extended to live on a variety of $J^2$. We are interested in the existence and behaviour of extensions of arbitrary Bianchi-Lie and variational vector fields acting on the Bianchi variety and accordingly we classify all such vector fields correspondin…
Linear hyperbolic equations in a double null foliation
本文研究双零叶层中的一阶线性双曲方程组，证明给定过去零超曲面初值时的全局存在唯一性，并据此揭示其与 Bianchi 方程及线性化方程的关系，导出新的逐点代数约束。
Lie group symmetry analysis for systems of coupled, nonlinear ordinary differential equations is performed in order to obtain the entire solution space to Einstein's field equations for vacuum Bianchi spacetime geometries. The symmetries used are the automorphisms of the Lie algebra of the corresponding three-dimensional isometry group acting on the hyper-surfaces of simultaneity for each Bianchi Type, as well as the scaling and the time reparametrization symmetry. A detailed application of the method is presented for Bianchi Type IV. The result is the acquisition of the general solution of Ty…
In this paper, we present the Noether symmetries of a class of the Bianchi type I anisotropic model in the context of f(T) gravity. By solving the system of equations obtained from the Noether symmetry condition, we obtain the form of f(T) as a teleparallel form. This analysis shows that teleparallel gravity has the maximum number of Noether symmetries. We derive the symmetry generators and show that there are five kinds of symmetries, including time and scale invariance under metric coefficients. We classify the symmetries and we obtain the corresponding invariants.
The quantization of the most general Bianchi Type II geometry -with all six scale factors, as well as the lapse function and the shift vector, present- is considered. In an earlier work, a first reduction of the initial 6-dimensional configuration space, to a 4-dimensional one, has been achieved by the usage of the information furnished by the quantum form of the linear constraints. Further reduction of the space in which the wave function -obeying the Wheeler-DeWitt equation- lives, is accomplished by unrevealling the extra symmetries of the Hamiltonian. These symmetries appear in the form of…
We consider the Bianchi identity as a field equation for the distortion of the shapes of images produced by weak gravitational lensing. Using the spin coefficient formalism of Newman and Penrose [1962], we show that certain complex components of the Weyl and Ricci curvature tensors are directly related to fundamental observables in weak gravitational lensing. In the case of weak gravitational fields, we then show that the Bianchi identity provides a field equation for the Ricci tensor assuming a known Weyl tensor. From the Bianchi identity, we derive the integral equation for weak lensing pres…
In this work, the quantization of the most general Bianchi Type I geometry, with and without a cosmological constant, is considered. In the spirit of identifying and subsequently removing as many gauge degrees of freedom as possible, a reduction of the initial 6--dimensional configuration space is presented. This reduction is achieved by imposing as additional conditions on the wave function, the quantum version of the --linear in momenta-- classical integrals of motion (conditional symmetries). The vector fields inferred from these integrals induce, through their integral curves, motions in t…
Though the Weyl tensor is a linear combination of the curvature tensor, Ricci tensor and Ricci scalar, it does not have all and only the Lie symmetries of these tensors since it is possible, in principle, that "asymmetries cancel". Here we investigate if, when and how the symmetries can be different. It is found that we can obtain a metric with a finite dimensional Lie algebra of Weyl symmetries that properly contains the Lie algebra of curvature symmetries. There is no example found for the converse requirement. It is speculated that there may be a fundamental reason for this lack of "duality…
In this paper we use Noether symmetries of the geodesic Lagrangian in Bianchi V spacetimes to study various cosmological solutions of Einstein's field equations. Our first result is the identification of the subalgebras of Noether symmetries of the equations of motions in such spacetimes with dimension 4, 5, 6, 7, 9 or 10 of the maximal algebra of Lie point symmetries of dimension 13. Secondly we give physical interpretation of new cosmological solutions which satisfy positive energy condition and yield critical bounds on the expansion coefficient $α$, in which the underlying non-flat spacetim…
The quantization of Class A Bianchi Type VI and VII geometries -with all six scale factors, as well as the lapse function and the shift vector present- is considered. A first reduction of the initial 6-dimensional configuration space is achieved by the usage of the information furnished by the quantum form of the linear constraints. Further reduction of the space in which the wave function -obeying the Wheeler-DeWitt equation- lives, is accomplished by revealing a classical integral of motion, tantamount to an extra symmetry of the corresponding classical Hamiltonian. This symmetry generator -…
An answer to the question: Can, in general, the adoption of a given symmetry induce a further symmetry, which might be hidden at a first level? has been attempted in the context of differential geometry of locally homogeneous spaces. Based on E. Cartan's theory of moving frames, a methodology for finding all symmetries for any n dimensional locally homogeneous space is provided. The analysis is applied to 3 dimensional spaces, whereby the embedding of them into a 4 dimensional Lorentzian manifold is examined and special solutions to Einstein's field equations are recovered. The analysis is mai…
We determine the conformal algebra of Bianchi III and Bianchi V spacetimes or, equivalently, we determine all Bianchi III and Bianchi V spacetimes which admit a proper conformal Killing vector. The algorithm that we use has been developed in Class. Quantum. Grav. 15, 2909 (1998) and concerns the computation of the CKVs of decomposable spacetimes. The main point of this method is that a decomposable space admits a CKV if the reduced space admits a gradient homothetic vector the latter being possible only if the reduced space is flat or a space of constant curvature. We apply this method in a st…
Lie symmetries of various geometrical and physical quantities in general relativity play an important role in understanding the curvature structure of manifolds. The Riemann curvature and Weyl tensors are two fourth-rank tensors in the theory. Interrelations between the symmetries of these two tensors (known as collineations) are studied. Some illustrative examples are also provided.
We present an analysis of the Kretschmann and Weyl squared scalars for the general Bianchi IX model filled with tilted dust. Particular attention is given to the asymptotic regime close to the singularity for which we provide heuristic considerations supported by numerical simulations. The present paper is an extension of our earlier publication [1].
We look for four dimensional Einstein-Weyl spaces equipped with a regular Bianchi metric. Using the explicit 4-parameters expression of the distance obtained in a previous work for non-conformally-Einstein Einstein-Weyl structures, we show that only four 1-parameter families of regular metrics exist on orientable manifolds : they are all of Bianchi $IX$ type and conformally Kähler ; moreover, in agreement with general results, they have a positive definite conformal scalar curvature. In a Gauduchon's gauge, they are compact and we obtain their topological invariants. Finally, we compare our re…
Spin-network states for the Bianchi I and IX cosmological models from quantum constrained symmetries
本文在量子层面实现规范固定条件，构造相应量子算符，证明均匀自旋网络态满足约束，从而在完整SU(2)对称的宇宙学理论与标准圈量子宇宙学之间建立联系。
The effects of noncommutativity in the phase-space of the classical and quantum cosmology of Bianchi models are investigated. Exact solutions in both commutative and noncommutative cases are presented and compared. Further, the Noether symmetries of the Bianchi class A spacetimes are studied in both cases and similarities and differences are discussed.
A twisted ${\mathcal C}^\star $- algebra of the extended (noncommutative) Heisenberg-Weyl group has been constructed which takes into account the Uncertainty Principle for coordinates in the Planck length regime. This general construction is then used to generate an appropriate Hilbert space and observables for the noncommutative theory which, when applied to the Bianchi I Cosmology, leads to a new set of equations that describe the quantum evolution of the universe. We find that this formulation matches theories based on a reticular Heisenberg-Weyl algebra in the bouncing and expanding region…
We study the late time evolution of a class of exact anisotropic cosmological solutions of Einstein's equations, namely spatially homogeneous cosmologies of Bianchi type VII$_0$ with a perfect fluid source. We show that, in contrast to models of Bianchi type VII$_h$ which are asymptotically self-similar at late times, Bianchi VII$_0$ models undergo a complicated type of self-similarity breaking. This symmetry breaking affects the late time isotropization that occurs in these models in a significant way: if the equation of state parameter $γ$ satisfies $γ\leq 4/3$ the models isotropize as regar…
We explore Noether gauge symmetries of FRW and Bianchi I universe models for perfect fluid in scalar-tensor gravity with extra term $R^{-1}$ as curvature correction. Noether symmetry approach can be used to fix the form of coupling function $ω(ϕ)$ and the field potential $V(ϕ)$. It is shown that for both models, the Noether symmetries, the gauge function as well as the conserved quantity, i.e., the integral of motion exist for the respective point like Lagrangians. We determine the form of coupling function as well as the field potential in each case. Finally, we investigate solutions through …
We present here the general transformation that leaves unchanged the form of the field equations for perfect fluid Friedmann--Robertson--Walker and Bianchi V cosmologies. The symmetries found can be used as algorithms for generating new cosmological models from existing ones. A particular case of the general transformation is used to illustrate the crucial role played by the number of scalar fields in the occurrence of inflation. Related to this, we also study the existence and stability of Bianchi V power law solutions.
The theory of symmetries of systems of coupled, ordinary differential equations (ODE) is used to develop a concise algorithm in order to obtain the entire space of solutions to vacuum Bianchi Einstein Field Equations (EFEs). The symmetries used are the well known automorphisms of the Lie algebra for the corresponding isometry group of each Bianchi Type, as well as the scaling and the time re-parametrization symmetry. The application of the method to Type VII_h results in (a) obtaining the general solution of Type VII_0 with the aid of the third Painlevé transcendental (b) obtaining the general…
We study the evolution of the Weyl curvature invariant in all spatially homogeneous universe models containing a non-tilted gamma-law perfect fluid. We investigate all the Bianchi and Thurston type universe models and calculate the asymptotic evolution of Weyl curvature invariant for generic solutions to the Einstein field equations. The influence of compact topology on Bianchi types with hyperbolic space sections is also considered. Special emphasis is placed on the late-time behaviour where several interesting properties of the Weyl curvature invariant occur. The late-time behaviour is class…
The concept of scale factor duality is considered within the context of the spatially homogeneous, vacuum Brans-Dicke cosmologies. In the Bianchi class A, it is found that duality symmetries exist for the types I, II, VI_0, VII_0, but not for types VIII and IX. The Kantowski-Sachs and locally rotationally symmetric Bianchi type III models also exhibit a scale factor duality, but no such symmetries are found for the Bianchi type V. In this way anisotropy and spatial curvature may have important effects on the nature of such dualities.
The locally rotationally symmetric tilted perfect fluid Bianchi type V cosmological model provides examples of future geodesically complete spacetimes that admit a `kinematic singularity' at which the fluid congruence is inextendible but all frame components of the Weyl and Ricci tensors remain bounded. We show that for any positive integer n there are examples of Bianchi type V spacetimes admitting a kinematic singularity such that the covariant derivatives of the Weyl and Ricci tensors up to the n-th order also stay bounded. We briefly discuss singularities in classical spacetimes.
In several of the class A Bianchi models, minisuperspaces admit symmetries. It is pointed out that they can be used effectively to complete the Dirac quantization program. The resulting quantum theory provides a useful platform to investigate a number of conceptual and technical problems of quantum gravity.
The (twice-contracted) second Bianchi identity is a differential curvature identity that holds on any smooth manifold with a metric. In the case when such a metric is Lorentzian and solves Einstein's equations with an (in this case inevitably smooth) energy-momentum-stress tensor of a "matter field" as the source of spacetime curvature, this identity implies the physical laws of energy and momentum conservation for the "matter field". The present work inquires into whether such a Bianchi identity can still hold in a weak sense for spacetimes with curvature singularities associated with timelik…
Noether Symmetry Analysis of the Klein--Gordon and Wave Equations in Bianchi I Spacetime
本文利用新的 Noether 对称关系分析 Bianchi I 时空中的 Klein–Gordon 方程及其波动方程特例，并导出对应守恒定律。
The Weyl curvature includes the Newtonian field and an additional field, the so-called anti-Newtonian. In this paper, we use the Bianchi and Ricci identities to provide a set of constraints and propagations for the Weyl fields. The temporal evolutions of propagations manifest explicit solutions of gravitational waves. We see that models with purely Newtonian field are inconsistent with relativistic models and obstruct sounding solutions. Therefore, both fields are necessary for the nonlocal nature and radiative solutions of gravitation.
The theory of symmetries of systems of coupled, ordinary differential equations (ODE's) is used to develop a concise algorithm for cartographing the space of solutions to vacuum Bianchi Einstein's Field Equations (EFE). The symmetries used are the well known automorphisms of the Lie algebra for the corresponding isometry group of each Bianchi Type, as well as the scaling and the time eparameterization symmetry. Application of the method to Type III results in: a) the recovery of all known solutions without prior assumption of any extra symmetry, b) the enclosure of the entire unknown part of t…
The Noether symmetry analysis is applied for the analysis of the field equations in an anisotropic background in $f(T,B)$-theory. We consider the $f\left( T,B\right) =T+F\left( B\right) $ which describes a small deviation from TEGR introduced by the boundary scalar $B$. For the Bianchi\ I, Bianchi III and Kantowski-Sachs geometries there exists a minisuperspace description and Noether's theorems are applied. We investigate the existence of invariant point transformations. We find that for the Bianchi I spacetime the gravitational field equations are Liouville integrable for the $F\left( B\righ…
Celestial $Lw_{1+\infty}$ charges from a twistor action
本文利用扭量空间框架，从自对偶引力的 Poisson BF 扭量作用量出发，第一性原理推导了天球 $Lw_{1+\infty}$ 对称性的正则生成元，并将其表示为类光无穷远处的面积分，从相空间角度阐明了该对称性。
The Weyl curvature hypothesis of Penrose attempts to explain the high homogeneity and isotropy, and the very low entropy of the early universe, by conjecturing the vanishing of the Weyl tensor at the Big-Bang singularity. In previous papers it has been proposed an equivalent form of Einstein's equation, which extends it and remains valid at an important class of singularities (including in particular the Schwarzschild, FLRW, and isotropic singularities). Here it is shown that if the Big-Bang singularity is from this class, it also satisfies the Weyl curvature hypothesis. As an application, we …
Generalized Eddington--Finkelstein Coordinates and Exact Vaidya-Type Solutions in Weyl Conformal Gravity
该研究在外尔共形引力框架下利用类Eddington--Finkelstein坐标，求出三类对称性下的全部真空动力学解并分析其性质，同时推导分类含库仑电场与零尘埃的非真空解，还探讨了规范等价性与相关定理的作用。
A higher dimensional frame formalism is developed in order to study implications of the Bianchi identities for the Weyl tensor in vacuum spacetimes of the algebraic types III and N in arbitrary dimension $n$. It follows that the principal null congruence is geodesic and expands isotropically in two dimensions and does not expand in $n-4$ spacelike dimensions or does not expand at all. It is shown that the existence of such principal geodesic null congruence in vacuum (together with an additional condition on twist) implies an algebraically special spacetime. We also use the Myers-Perry metric …
The background field method is used to linearize the Weyl invariant scalar-tensor gravity, coupled with a Stueckelberg field. For a generic background metric, this action is found to be not invariant, under both diffeomorphism and generalized Weyl symmetry, the latter being a combination of gauge and Weyl transformations. Interestingly, the quadratic Lagrangian, emerging from a background of Minkowski metric, respects both the transformations, independently. Becchi-Rouet-Stora-Tyutin (BRST) symmetry of scalar-tensor gravity coupled with a Stueckelberg-like massive gauge particle, possessing di…
Symmetries and Charges in Weyl-Fefferman-Graham Gauge
研究三维AdS爱因斯坦引力在Weyl-Fefferman-Graham规范下的渐近对称性，指出该规范是陈-西蒙斯表述中规范固定的自然中间步骤，证明转换到常规Fefferman-Graham规范的微分同胚可带荷，并从全息重整化与变分原理角度给出该规范及其荷的新全息视角。
In this paper we study the cosmological dynamics of Randall-Sundrum braneworld type scenarios in which the five-dimensional Weyl tensor has a non-vanishing projection onto the three-brane where matter fields are confined. Using dynamical systems techniques, we study how the state space of Friedmann-Lemaitre-Robertson-Walker (FLRW) and Bianchi type I scalar field models with an exponential potential is affected by the bulk Weyl tensor, focusing on the differences that appear with respect to standard general relativity and also Randall-Sundrum cosmological scenarios without the Weyl tensor contr…
We present the general solution to the Plebanski equation for an H-space that admits Killing vectors for an entire SU(2) of symmetries, which is therefore also the general solution of the sDiff(2)Toda equation that allows these symmetries. Desiring these solutions as a bridge toward the future for yet more general solutions of the sDiff(2)Toda equation, we generalize the earlier work of Olivier, on the Atiyah-Hitchin metric, and re-formulate work of Babich and Korotkin, and Tod, on the Bianchi IX approach to a metric with an SU(2) of symmetries. We also give careful delineations of the conform…
We analyze the phase space of Bianchi I cosmologies filled by a spin fluid in the framework of $f(R)$-gravity with torsion using a combination of the dynamical systems approach and the 1+3 covariant formalism. In the simple case of $f(R)=R^n$ our results allow a quantification of the role of torsion and the spin of the cosmic fluid in the evolution of the cosmology. While torsion is able to modify the cosmological dynamics with respect to the purely metric case, the spin has little influence on the cosmology. We argue that this is due to the different symmetries of the tensor characterizing th…
Killing tensors of Weyl's class
本研究以Weyl类静态轴对称时空为对象，利用秩2 Killing张量标准型推导其隐藏对称性约束，明确其完全可积性与Killing张量的关联，为Petrov I型时空隐藏对称性研究提供系统工具。
We revise and generalize the properties of the electric and the magnetic scalar potentials in spacetimes admitting a Killing vector field: Their constancy on the Killing horizons, uniqueness of solution for the electromagnetic test fields and the relation between the Bianchi identity and Maxwell's equations. In each of these examples, collinearity of currents with the Killing vector field is shown to be the crucial property.
We study several cosmological models with Bianchi \textrm{VI}$_{0}$ symmetries under the self-similar approach. In order to study how the \textquotedblleft constants\textquotedblright\ $G$ and $Λ$ may vary, we propose three scenarios where such constants are considered as time functions. The first model is a perfect fluid. We find that the behavior of $G$ and $Λ$ are related. If $G$ behaves as a growing time function then $Λ$ is a positive decreasing time function but if $G$ is decreasing then $Λ$ is negative. For this model we have found a new solution. The second model is a scalar field, whe…
In this paper we deal with the cosmological dynamics of Randall-Sundrum brane-world type scenarios in which the five-dimensional Weyl tensor has a non-vanishing projection onto the three-brane where matter fields are confined. Using dynamical systems techniques, we study how the state space of Friedmann-Lemaitre-Robertson-Walker (FLRW) and Bianchi type I cosmological models is affected by the bulk Weyl tensor, focusing in the differences that appear with respect to general relativity and also Randall-Sundrum cosmological scenarios without the Weyl tensor contribution.
We analyze type I vacuum solutions admitting an isometry whose Killing 2--form is aligned with a principal bivector of the Weyl tensor, and we show that these solutions belong to a family of type I metrics which admit a group $G_3$ of isometries. We give a classification of this family and we study the Bianchi type for each class. The classes compatible with an aligned Killing 2--form are also determined. The Szekeres-Brans theorem is extended to non vacuum spacetimes with vanishing Cotton tensor.
We show that the asymptotic infinite dimensional enlarged gauge symmetries constructed for QED are anomalous in Dirac and Weyl semimetals. This symmetry is particularly important in particle physics for its analogy with the Bondi-Metzner-Sachs (BMS) symmetries in gravity, as well as for its connection with QED soft IR theorems. This leads to observable effects, because of the induction of a new current in the material, which carries a memory of the BMS symmetry precursor.
We consider four (real or complex) dimensional hyper-Kähler metrics with a conformal symmetry K. The three-dimensional space of orbits of K is shown to have an Einstein-Weyl structure which admits a shear-free geodesics congruence for which the twist is a constant multiple of the divergence. In this case the Einstein-Weyl equations reduce down to a single second order PDE for one function. The Lax representation, Lie point symmetries, hidden symmetries and the recursion operator associated with this PDE are found, and some group invariant solutions are considered.
Relativistic modeling of cosmological structures with Bianchi IX spacetimes
本文提出一种相对论框架，通过将精确的 Bianchi IX 时空与正曲率 FLRW 宇宙区域匹配，利用精确解追踪一般初始密度扰动的非线性演化，克服了标准微扰理论与高度对称解的局限。
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