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1.
We formulate two global existence conjectures for the Einstein equations and discuss their relevance to the cosmic censorship conjecture. We argue that the reformulation of the cosmic censorship conjecture as a global existence problem renders it more amenable to direct analytical attack. To demonstrate the facilty of this approach we prove the cosmological version of our global existence conjecture for the Gowdy spacetimes onT 3×R.  相似文献   

2.
The group of conformal diffeomorphisms and the group of causal automorphisms on two-dimensional globally hyperbolic spacetimes are clarified. It is shown that if two-dimensional spacetimes have non-compact Cauchy surfaces, then the groups are subgroups of that of two-dimensional Minkowski spacetime, and if two-dimensional spacetimes have compact Cauchy surfaces, then the groups are subgroups of that of two-dimensional Einstein’s static universe. Also, the groups of such spacetimes are explicitly calculated by use of universal covering spaces.  相似文献   

3.
We prove two theorems, announced in [6], for static spacetimes that solve Einstein's equation with negative cosmological constant. The first is a general structure theorem for spacetimes obeying a certain convexity condition near infinity, analogous to the structure theorems of Cheeger and Gromoll for manifolds of non-negative Ricci curvature. For spacetimes with Ricci-flat conformal boundary, the convexity condition is associated with negative mass. The second theorem is a uniqueness theorem for the negative mass AdS soliton spacetime. This result lends support to the new positive mass conjecture due to Horowitz and Myers which states that the unique lowest mass solution which asymptotes to the AdS soliton is the soliton itself. This conjecture was motivated by a nonsupersymmetric version of the AdS/CFT correspondence. Our results add to the growing body of rigorous mathematical results inspired by the AdS/CFT correspondence conjecture. Our techniques exploit a special geometric feature which the universal cover of the soliton spacetime shares with familiar ``ground state' spacetimes such as Minkowski spacetime, namely, the presence of a null line, or complete achronal null geodesic, and the totally geodesic null hypersurface that it determines. En route, we provide an analysis of the boundary data at conformal infinity for the Lorentzian signature static Einstein equations, in the spirit of the Fefferman-Graham analysis for the Riemannian signature case. This leads us to generalize to arbitrary dimension a mass definition for static asymptotically AdS spacetimes given by Chruciel and Simon. We prove equivalence of this mass definition with those of Ashtekar-Magnon and Hawking-Horowitz.  相似文献   

4.
In the differential geometry of certain F-structures, the importance of concircular curvature tensor is very well known. The relativistic significance of this tensor has been explored here. The spacetimes satisfying Einstein field equations and with vanishing concircular curvature tensor are considered and the existence of Killing and conformal Killing vectors have been established for such spacetimes. Perfect fluid spacetimes with vanishing concircular curvature tensor have also been considered. The divergence of concircular curvature tensor is studied in detail and it is seen, among other results, that if the divergence of the concircular tensor is zero and the Ricci tensor is of Codazzi type then the resulting spacetime is of constant curvature. For a perfect fluid spacetime to possess divergence-free concircular curvature tensor, a necessary and sufficient condition has been obtained in terms of Friedmann-Robertson-Walker model.  相似文献   

5.
The null-surface formulation of general relativity (NSF) describes gravity by using families of null surfaces instead of a spacetime metric. Despite the fact that the NSF is (to within a conformal factor) equivalent to general relativity, the equations of the NSF are exceptionally difficult to solve, even in 2+1 dimensions. The present paper gives the first exact \((2+1)\)-dimensional solution that depends nontrivially upon all three of the NSF’s intrinsic spacetime variables. The metric derived from this solution is shown to represent a spacetime whose source is a massless scalar field that satisfies the general relativistic wave equation and the Einstein equations with minimal coupling. The spacetime is identified as one of a family of \((2+1)\)-dimensional general relativistic spacetimes discovered by Cavaglià.  相似文献   

6.
We consider the static and spherically symmetric field equations of general relativity for charged perfect fluid spheres in the presence of a cosmological constant. Following work by Florides (J Phys A Math Gen 16:1419–1433, 1983) we find new exact solutions of the field equations, and discuss their mass radius ratios. These solutions, for instance, require the charged Nariai metric to be the vacuum part of the spacetime. We also find charged generalizations of the Einstein static universe and speculate that the smallness problem of the cosmological constant might become less problematic if charge is taken into account.  相似文献   

7.
Beltrami-de Sitter时空和de Sitter不变的狭义相对论   总被引:4,自引:0,他引:4       下载免费PDF全文
郭汉英  黄超光  田雨  徐湛  周彬 《物理学报》2005,54(6):2494-2504
分析了在相对论体系中狭义相对性原理和宇宙学原理之间的关系以及Beltrami-de Sitter -陆启铿疑难.指出可以把狭义相对性原理推广到非零常曲率时空,在具有Beltrami度规 的de Sitter/反de Sitter时空中建立狭义相对论的运动学和粒子动力学. 在这类狭义相对 论中,相对于Beltrami坐标同时性,Beltrami坐标系就是惯性坐标系,相应的观测者为惯 性观测者; 对于自由粒子和光讯号, 惯性定律成立;可以定义可观测量,它们不但守恒而且还 满足推广的爱因斯坦关系.除了Beltrami坐标时同时性之外,对于共动观测, 还可以取固 有时同时性;此时,Beltrami度规成为Robertson-Walker型的度规,其3维空间是闭的,对 于平坦的偏离为宇宙学常数的量级.这表明,在这类狭义相对论中,相对性原理与“完美”宇 宙学原理之间存在内在联系,并不存在那些问题.进而,基于最新观测事实,重述了Mach原 理;指出对于Beltrami-de Sitter/反de Sitter时空,宇宙学常数恰恰给出惯性运动的起 源. 关键词: 狭义相对性原理 宇宙学原理 de Sitter不变的狭义相对论 Beltrami-de Sitter时空 同时性 Mach原理  相似文献   

8.
Extremely compact stars (ECS) (having radius R < 3GM/c 2) contain captured null geodesics. Certain part of neutrinos produced in their interior will be trapped, influencing thus their neutrino luminosity and thermal evolution. The trapping effect has been previously investigated for the internal Schwarzschild spacetimes with the uniform distribution of energy density. Here, we extend our earlier study considering the influence of the cosmological constant Λ on the trapping phenomena. Our model for the interior of ECS is based on the internal Schwarzschild-(anti-)de Sitter (S(a)dS) spacetimes with uniform distribution of energy density matched to the external vacuum S(a)dS spacetime with the same cosmological constant. Assuming uniform and isotropic distribution of local neutrino emissivity we determine behavior of the trapping coefficients, i.e., “global” one representing influence on the neutrino luminosity and “local” one representing influence on the cooling process. We demonstrate that the repulsive (attractive) cosmological constant has tendency to enhance (damp) the trapping phenomena.  相似文献   

9.
Using quantum field theory in black hole-type spacetimes with horizons, which includes all the black hole solutions and also some other interesting solutions in general relativity, we obtain Hawking's thermal spectrum of Dirac particles near the event horizon as well as the cosmological horizon of the spacetime.  相似文献   

10.
We discuss a class of (local and non-local) theories of gravity that share same properties: (i) they admit the Einstein spacetime with arbitrary cosmological constant as a solution; (ii) the on-shell action of such a theory vanishes and (iii) any (cosmological or black hole) horizon in the Einstein spacetime with a positive cosmological constant does not have a non-trivial entropy. The main focus is made on a recently proposed non-local model. This model has two phases: with a positive cosmological constant Λ>0Λ>0 and with zero Λ. The effective gravitational coupling differs essentially in these two phases. Generalizing the previous result of Barvinsky we show that the non-local theory in question is free of ghosts on the background of any Einstein spacetime and that it propagates a standard spin-2 particle. Contrary to the phase with a positive Λ, where the entropy vanishes for any type of horizon, in an Einstein spacetime with zero cosmological constant the horizons have the ordinary entropy proportional to the area. We conclude that, somewhat surprisingly, the presence of any, even extremely tiny, positive cosmological constant should be important for the proper resolution of the entropy problem and, possibly, the information puzzle.  相似文献   

11.
We consider the maximal subgroups of the conformai group (which have in common as a subgroup the group of pure spatial rotations) as isometry groups of conformally flat spacetimes. We identify the corresponding cosmological solutions of Einstein's field equations. For each of them, we investigate the possibility that it could be generated by anSU (2) Yang-Mills field built, via the Corrigan-Fairlie-'t Hooft-Wilczek ansatz, from a scalar field identical with the square root of the conformal factor defining the space-time metric tensor. In particular, the Einstein cosmological model can be generated in this manner, but in the framework of strong gravity only, a micro-Einstein universe being then viewed as a possible model for a hadron.Boursier A.G.C.D.  相似文献   

12.
We show that for four-dimensional spacetimes with a non-null hypersurface orthogonal Killing vector and for a Chern–Simons (CS) background (non-dynamical) scalar field, which is constant along the Killing vector, the source-free equations of CS modified gravity decouple into their Einstein and Cotton constituents. Thus, the model supports only general relativity solutions. We also show that, when the cosmological constant vanishes and the gradient of the CS scalar field is parallel to the non-null hypersurface orthogonal Killing vector of constant length, CS modified gravity reduces to topologically massive gravity in three dimensions. Meanwhile, with the cosmological constant such a reduction requires an appropriate source term for CS modified gravity.  相似文献   

13.
Some important spacetimes are conformally flat; examples are the Robertson–Walker cosmological metric, the Einstein–de Sitter spacetime, and the Levi-Civita–Bertotti–Robinson and Mannheim metrics. In this paper we construct generic thin shells in conformally flat spacetime supported by a perfect fluid with a linear equation of state, i.e., \(p=\omega \sigma .\) It is shown that, for the physical domain of \(\omega \), i.e., \(0<\omega \le 1\), such thin shells are not dynamically stable. The stability of the timelike thin shells with the Mannheim spacetime as the outer region is also investigated.  相似文献   

14.
We prove the existence of maximal surfaces in asymptotically flat spacetime satisfying an interior condition. This uses a priori estimates which can also be applied to prescribed mean curvature surfaces in cosmological spacetimes and the Dirichlet problem.  相似文献   

15.
To include all types of singularities into a geometrically tractable theoretical scheme we change from Einstein algebras, an algebraic generalization of general relativity, to sheaves of Einstein algebras. The theory of such spaces, called Einstein structured spaces, is developed. Both quasiregular and curvature singularities are studied in some detail. Examples of the closed Friedmann world model and the Schwarzschild spacetime show that Schmidt'sb-boundary is a useful theoretical tool when considered in the category of structured spaces.  相似文献   

16.
17.
We discuss the failure of general relativity to provide a proper Newtonian limit when the spacetime dimensionality is reduced to 2+1 and try to bypass this difficulty by assuming alternative equations for the gravitational field. We investigate the properties of spacetimes generated by circularly symmetric matter distributions in two cases: weakening Einstein equations, and by considering the Brans-Dicke theory of gravity. A comparison with the corresponding Newtonian picture is made.  相似文献   

18.
Consider a globally hyperbolic cosmological spacetime. Topologically, the spacetime is then a compact 3-manifold in cartesian product with an interval. Assuming that there is an expanding direction, is there any relation between the topology of the 3-manifold and the asymptotics? In fact, there is a result by Michael Anderson, where he obtains relations between the long-time evolution in General Relativity and the geometrization of 3-manifolds. In order to obtain conclusions however, he makes assumptions concerning the rate of decay of the curvature as proper time tends to infinity. It is thus of interest to find out if such curvature decay conditions are always fulfilled. We consider here the Gowdy spacetimes, for which we prove that the decay condition holds. However, we observe that for general Bianchi VIII spacetimes, the curvature decay condition does not hold, but that some aspects of the expected asymptotic behaviour are still true.  相似文献   

19.
We consider a $D$ D dimensional Kasner type diagonal spacetime where metric functions depend only on a single coordinate and electromagnetic field shares the symmetries of spacetime. These solutions can describe static cylindrical or cosmological Einstein–Maxwell vacuum spacetimes. We mainly focus on electrovacuum solutions and four different types of solutions are obtained in which one of them has no four dimensional counterpart. We also consider the properties of the general solution corresponding to the exterior field of a charged line mass and discuss its several properties. Although it resembles the same form with four dimensional one, there is a difference on the range of the solutions for fixed signs of the parameters. General magnetic field vacuum solution are also briefly discussed, which reduces to Bonnor-Melvin magnetic universe for a special choice of the parameters. The Kasner forms of the general solution are also presented for the cylindrical or cosmological cases.  相似文献   

20.
Classification of conformally flat n-dimensional pseudo-Riemannian spaces via Plebanski's method is discussed. It is based on embedding these spaces into a flat (n + 2)-dimensional space and on finding their minimal isometry groups which are subgroups of the conformal group. In particular, the case n = 4 is given in full detail and compared with incomplete results known in the literature. The found conformally flat spacetimes are identified with the associated solutions of the Einstein equations and with the spacetimes used in various cosmological considerations.  相似文献   

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