物质纯重力场部分的能量-动量张量研究

认为物质的质量(能量)存在形式可分为两部分，一部分是以纯物质形式存在的，另一部分是以纯重力场形式存在的.物质质量(能量)这两种形式各自对应着相应的能量 动量张量，物质总的能量-动量张量可表示为Tμν=T(Ⅰ)μν+T(Ⅱ)μν,这里，T(Ⅰ)μν，T（Ⅱ）μν分别代表物质纯物质部分和纯重力场部分的能量-动量张量.通过类比电磁理论，定义：ωμ≡-c2gμ0/g00,并引入一个反对称张量Dμν=ωμ/xν-ων/xμ，则物质纯重力场部分的能量-动量张量为T(Ⅱ)μν=(DμρDρν-gμνDαβDαβ/4 关键词： 能量-动量张量 纯重力场 重力场方程 标量重力势 矢量重力势     

Stability of Relative Equilibria. Part II: Dumbell Satellites

In the second part a practically important problem, namely the stability of relative equilibria of a dumbell satellite on an orbit around the Earth is treated by means of the reduced energy-momentum method. The dumbell satellite is used to emphasize the advantages of the reduced energy-momentum method which did not become obvious in the simple example of the rotating pendulum treated in Part I, as well as, to discuss some of the finer technical details.     

静态球对称黑洞热力学与爱因斯坦场方程

建立在广义相对论基础上的黑洞理论与热力学定律之间有着深刻的内在联系.具体考虑球对称黑洞,研究表明通过史瓦西黑洞和Reissner-Nordstrom黑洞在其视界附近的爱因斯坦场方程可以直接得到对应的黑洞热力学第一定律.这揭示了爱因斯坦引力场方程与黑洞热力学的关系,表明了在广义相对论理论框架下黑洞热力学规律的必然性.     

On Cavitation, Configurational Forces and Implications for Fracture in a Nonlinearly Elastic Material

Experiments on polymers indicate that large tensile stress can induce cavitation, that is, the appearance of voids that were not previously evident in the material. This phenomenon can be viewed as either the growth of pre-existing infinitesimal holes in the material or, alternatively, as the spontaneous creation of new holes in an initially perfect body. In this paper our approach is to adopt both views concurrently within the framework of the variational theory of nonlinear elasticity. We model an elastomer on a macroscale as a void-free material and, on a microscale, as a material containing certain defects that are the only points at which hole formation can occur. Mathematically, this is accomplished by the use of deformations whose point singularities are constrained. One consequence of this viewpoint is that cavitation may then take place at a point that is not energetically optimal. We show that this disparity will generate configurational forces, a type of force identified previously in dislocations in crystals, in phase transitions in solids, in solidification, and in fracture mechanics. As an application of this approach we study the energetically optimal point for a solitary hole to form in a homogeneous and isotropic elastic ball subject to radial boundary displacements. We show, in particular, that the center of the ball is the unique optimal point. Finally, we speculate that the configurational force generated by cavitation at a non-optimal material point may be sufficient to result in the onset of fracture. The analysis utilizes the energy-momentum tensor, the asymptotics of an equilibrium solution with an isolated singularity, and the linear theory of elasticity at the stressed configuration that the body occupies immediately prior to cavitation. This revised version was published online in June 2006 with corrections to the Cover Date.     

Møller’s Energy-Momentum Complex for a Spacetime Geometry on a Noncommutative Curved D3-Brane

Møller’s energy-momentum complex is employed in order to determine the energy and momentum distributions for a spacetime described by a “generalized Schwarzschild” geometry in (3+1)-dimensions on a noncommutative curved D3-brane in an effective, open bosonic string theory. The geometry considered is obtained by an effective theory of gravity coupled with a nonlinear electromagnetic field and depends only on the generalized (effective) mass and charge which incorporate corrections of first order in the noncommutativity parameter.     

The leakage criterions of thin-wall pressure vessels,materials of missile and spacecraft

This paper presents the development of three leadage criterions to predict fracture in thin-wall pressure vessels, materials of missile and spaceraft. Experimental results show that the criterions are successful.I. Notation P internal pressure kg/mm² - _b critical stress kg/mm² - t wall thickness mm - r internal radius mm - t _o wall thickness at crack tip mm - r _o internal radius at crack tip mm - _B yield strength kg/mm² - _H circumferential stress at the yield tange of the crack tip kg/mm² - n rate of strain gardening - 2c length of surface-crack mm - a depth of surface-crack mm - L length of testing piece mm - K, C, B, aA constant     

On the gravitational angular momentum of rotating sources

The gravitational energy–momentum and angular momentum satisfy the algebra of the Poincaré group in the full phase space of the teleparallel equivalent of general relativity. The expression for the gravitational energy–momentum may be written as a surface integral in the three-dimensional spacelike hypersurface, whereas the definition for the angular momentum is given by a volume integral. It turns out that in practical calculations of the angular momentum of the gravitational field generated by localized sources like rotating neutron stars, the volume integral reduces to a surface integral, and the calculations can be easily carried out. Similar to previous investigations in the literature, we show that the total angular momentum is finite provided a certain asymptotic behaviour is verified. We discuss the dependence of the gravitational angular momentum on the frame, and argue that it is a measure of the dragging of inertial frames.     

Energy Distribution for a Power Model of the Plane Symmetric Spacetime in f(R) Gravity

The study of the energy localization in f(R) theories of gravity has attracted much interest in recent years. In this paper, the vacuum solutions of the modified field equations for a power model of plane symmetric metric are studied in metric f(R) gravity with the assumption of constant Ricci scalar. Next, we determine the energy-momentum complexes in f(R) theories of gravity for this spacetime for some important models. We also show that these models satisfy the stability and constant curvature conditions.     

Energy and momentum of general spherically symmetric frames on the regularizing teleparallelism

In the context of the covariant teleparallel framework, we use the 2-form translational momentum to compute the total energy of two general spherically symmetric frames. The first one is characterized by an arbitrary function H(r), which preserves the spherical symmetry and reproduces all the previous solutions, while the other one is characterized by a parameter ξ which ensures the vanishing of the axial of trace of the torsion. We calculate the total energy by using two procedures, i.e., when the Weitzenböck connection Γ_α^β is trivial, and show how H(r) and ξ play the role of an inertia that leads the total energy to be unphysical. Therefore, we take into account Γ_α^β and show that although the space×we use contain an arbitrary function and one parameter, they have no effect on the form of the total energy and momentum as it should be.