Astrophysically significant solutions of the Einstein and Einstein-Maxwell equations from the Laplace’s seed

The stationary solutions given by Amenedo and Manko generated from known solutions of Laplace’s equation as seed have been generalised to include the electromagnetic field. Further, the exterior solution of an axially symmetric rotating body with higher multipole moments and a solution corresponding to a Kerr object embedded in a gravitational field are given. We also give a method for constructing stationary vacuum solutions from static magnetovac solutions and vice versa and discuss a specific application of this method.     

Letter: Spatial Metrics Which are Static in Many Ways

We consider Riemannian 3-metrics which can form the spatial part of vacuum solutions of the Einstein equations, possibly with a cosmological constant, in more than one way (in a sense made precise). The locally rotationally symmetric (LRS) Kasner metric gives the simplest example, and we find that the resulting space-time metrics are always of Petrov type D.     

Exact Solutions for Einstein＇s Hyperbolic Geometric Flow

In this paper we investigate the Einstein＇s hyperbolic geometric flow and obtain some interesting exact solutions for this kind of flow. Many interesting properties of these exact solutions have also been analyzed and we believe that these properties of Einstein＇s hyperbolic geometric flow are very helpful to understanding the Einstein equations and the hyperbolic geometric flow.     

Chemistry in Lasers. IX. Reexamination of the Einstein Coefficients and Two Level Population Inversion

From a re-examination of the Einstein coefficients in terms of current theory the common assumption that population inversion cannot be maintained in a two level system by optical pumping is shown to be erroneous. The nonisotropy of the radiative ensemble in an optical resonant cavity, absent from the original derivation by Einstein, is shown to be of decisive importance.     

爱因斯坦对量子理论发展的重要影响

结合20世纪量子力学发展的特殊历史背景,从早期的量子论到现行量子力学理论体系的形成和完善过程出发,讨论了爱因斯坦在量子力学方面的重要工作,指出他在量子理论发展的不同时期都发挥了重要作用,对量子力学理论的研究产生了重要而又深远的影响,极大地促进了量子力学的发展.     

The Taub solution again

A work, recently published by this journal, is discussed and the critique is presented in this same issue. Our revision of this critique is focused on two main topics: a) the suggested Taub solution and (b) the method followed to arrive at it.Reply to the comment by R. Jantzen, GRG 37 (2005)     

Classification of Nilsoliton metrics in dimension seven

The aim of this paper is to classify Ricci soliton metrics on 7-dimensional nilpotent Lie groups. It can be considered as a continuation of our paper in Fernández Culma (2012). To this end, we use the classification of 7-dimensional real nilpotent Lie algebras given by Ming-Peng Gong in his Ph.D thesis and some techniques from the results of Michael Jablonski (2010, 2012) and of Yuri Nikolayevsky (2011). Of the 9 one-parameter families and 140 isolated 7-dimensional indecomposable real nilpotent Lie algebras, we have 99 nilsoliton metrics given in an explicit form and 7 one-parameter families admitting nilsoliton metrics.Our classification is the result of a case-by-case analysis, so many illustrative examples are carefully developed to explain how to obtain the main result.     

Diagonalizing cohomogeneity-one Einstein metrics

We investigate when it is possible to globally diagonalize an Einstein metric of cohomogeneity-one under the action of a compact connected Lie group G with isotropy subgroup K. Restricting our attention to the non-monotypic case in which cohomogeneity-one metrics are not automatically diagonalizable, we make use of a subset of the ODEs of the Einstein condition to globally diagonalize the Einstein metric in certain cases. The program we use is inspired by a result well-known to relativists which states that Einstein metrics must be diagonalizable in the Bianchi IX case. We present a full classification of all the cohomogeneity-one metrics on which this method can be used.     

Algebraically special hypersurface-homogeneous Einstein spaces in general relativity

This paper illustrates the value of the Newman—Penrose complex null tetrad formalism by using it to obtain all algebraically special Einstein spaces admitting three-parameter groups of motions acting on timelike surfaces containing the repeated principal null direction. Taken together with earlier work, this enables us to give a complete list of Einstein spaces which are both algebraically special and hypersurface-homogeneous or homogeneous.     

Spin Zero Quantum Relativistic Particles in Einstein Universe

We find exact eigenvalues and eigenfunctions of relativistic massless scalar particle conformally coupled to a background Einstein universe.     

Cohomological uniqueness of the Cauchy problem solutions for the Einstein–Maxwell equation

In this paper we analyze the Cauchy problem for the Einstein–Maxwell equation in the case of non-characteristic initial hypersurface. To find the correct notions of characteristic and Cauchy data we introduce a complex, which we call the Einstein–Maxwell complex. Then the Cauchy problem acquires correctness in terms of an associated spectral sequence. We define a Cauchy data in such way that they allow us to reconstruct a cohomologously unique formal solution.     

On Mobility and Einstein Relation for Tracers in Time-Mixing Random Environments

In this paper we rigorously establish the existence of the mobility coefficient for a tagged particle in a simple symmetric exclusion process with adsorption/desorption of particles, in a presence of an external force field interacting with the particle. The proof is obtained using a perturbative argument. In addition, we show that, for a constant external field, the mobility of a particle equals to the self-diffusivity coefficient, the so-called Einstein relation. The method can be applied to any system where the environment has a Markovian evolution with a fast convergence to equilibrium (spectral gap property). In this context we find a necessary relation between forward and backward velocity for the validity of the Einstein relation. This relation is always satisfied by reversible systems. We provide an example of a non-reversible system, where the Einstein relation is valid.This revised version was published online in March 2005 with corrections to the page numbers.     

Comments on “quantum theory does not require action at a distance”

Kraus claims that the argument for action at a distance depends upon the classical prejudice that a measurement always measures something that already exists. It is shown that in the example considered by Kraus no assumption about pre-existing results is needed. A criterion proposed by Kraus for a theory to be compatible with locality is shown to be untenable.     

Generalized Einstein manifolds

A Finslerian manifold is called a generalized Einstein manifold (GEM) if the Ricci directional curvature R(u,u) is independent of the direction. Let F⁰(M, g_t) be a deformation of a compact n-dimensional Finslerian manifold preserving the volume of the unitary fibre bundle W(M). We prove that the critical points g₀ F⁰(g_t) of the integral I(g_t) on W(M) of the Finslerian scalar curvature (and certain functions of the scalar curvature) define a GEM. We give an estimate of the eigenvalues of Laplacian Δ defined on W(M) operating on the functions coming from the base when (M, g) is of minima fibration with a constant scalar curvature H admitting a conformal infinitesimal deformation (CID). We obtain λ ≥ H/(n − 1) (Δf = λf). If M is simply connected and λ = H/(n − 1), then (M, g) is Riemannian and is isometric to an n-sphere. We first calculate, in the general case, the formula of the second variationals of the integral I (g_t) for G = g₀, then for a CID we show that for certain Finslerian manifolds, I″(g₀) > 0. Applications to the gravitation and electromagnetism in general relativity are given. We prove that the spaces characterizing Einstein-Maxwell equations are GEMs.     

浪漫主义艺术家爱因斯坦--纪念狭义相对论创立100周年

本文从叙述滑稽大师卓别林称谓爱因斯坦是一位“浪漫主义艺术家”的轶闻趣事出发，深刻地论证了音乐艺术对物理科学的思维启迪。     

Note: An Unusual Route to General Relativity Equation in Presence of Dust in Irrotational Motion

We show that the general relativity theory equation, in presence of pressureless matter (dust) in irrotational motion, can be recovered from a scalar-tensor like variational approach. In this approach, the kinetic energy, , of a dynamical scalar field , couples directly to gravity. The lagrangian, exempt of explicit matter term, is varied in the framework of the first order formalism, and a conformal transformation, restoring riemannian geometry, is made. In this approach, it turns out that a non-empty spacetime is necessarily four-dimensional.     

From 2-dimensional surfaces to cosmological solutions

We construct perfect fluid metrics with two symmetries by means of a recently developed geometrical method [1]. The Einstein equations are reduced to a single equation for a conformal factor. Under additional assumptions we obtain new cosmological solutions of Bianchi type II, VI₀ and VII₀. The solutions depend on an arbitrary function of time, which can be specified in order to satisfy an equation of state.     

Letter: Parametrization of the Kerr-NUT Solution

The dragging of the Kerr-NUT solution does not tend to zero at infinity. To modify this solution in order to produce a good asymptotic behaviour we transform it by introducing two further parameters with the aid of a SU(1,1) transformation followed by a unitary transformation. By imposing a certain relation between these parameters we obtain a new solution with a good asymptotic behaviour for any value of l, the NUT parameter. The new solution corresponds to a parametrized Kerr solution and we show that l is linked to the form of its ergosphere.     

Schlesinger System,Einstein Equations and Hyperelliptic Curves

We review recent developments in the method of algebro-geometric integration of integrable systems related to deformations of algebraic curves. In particular, we discuss the theta-functional solutions of the Schlesinger system, Ernst equation, and self-dual SU(2)-invariant Einstein equations.     

光晶格中玻色-爱因斯坦凝聚体的自旋和磁研究

近年应用光晶格（optical lattice)控制原子玻色－爱因斯坦凝聚体（BEC）的研究取得了突破性的进展。德国Munich研究小组首次在三维光晶格中观察到了超冷原子从BEC超流状态向Mott insulator状态的量子相变。这样的量子相变现象不仅具有重大的理论研究价值，而且为BEC的实际应用提供了新的途径。文章介绍了作者近来在光晶格中BEC的自旋和磁特性方面的一些研究进展，并探讨了它们在磁传感器及量子计算中的可能应用。