离散时空中的非塌缩的尘埃球解

引进了实数的层次性与离散化，将连续函数理论加以改进和推广为离散函数理论，并基于由离散函数理论所表示的经典广义相对论来讨论尘埃物质的引力塌缩问题，指出了关于这个问题的连续体系的Oppenheimer 和Snyder解中的Friedmann内解与Schwarzschild外解的不完整性并加以拓展和离散化，导出了一种非塌缩的尘埃物质结构，消除了引力奇性并揭示了时空离散化的深刻性质. 关键词： 离散实数 离散时空 广义相对论 Oppenheimer 和Snyder解 奇性自由     

Embedding of Particle Waves in a Schwarzschild Metric Background

The special and general relativity theories are used to demonstrate that the velocity of an unradiative particle in a Schwarzschild metric background, and in an electrostatic field, is the group velocity of a wave that we call a particle wave, which is a monochromatic solution of a standard equation of wave motion and possesses the following properties. It generalizes the de Broglie wave. The rays of a particle wave are the possible particle trajectories, and the motion equation of a particle can be obtained from the ray equation. The standing particle wave equation generalizes the Schrödinger equation of wave amplitudes. The particle wave motion equation generalizes the Klein–Gordon equation; this result enables us to analyze the essence of the particle wave frequency. The equation of the eikonal of a particle wave generalizes the Hamilton–Jacobi equation; this result enables us to deduce the general expression for the linear momentum. The Heisenberg uncertainty relation expresses the diffraction of the particle wave, and the uncertainty relation connecting the particle instant of presence and energy results from the fact that the group velocity of the particle wave is the particle velocity. A single classical particle may be considered as constituted of geometrical particle wave; reciprocally, a geometrical particle wave may be considered as constituted of classical particles. The expression for a particle wave and the motion equation of the particle wave remain valid when the particle mass is zero. In that case, the particle is a photon, the particle wave is a component a classical electromagnetic wave that is embedded in a Schwarzschild metric background, and the motion equation of the wave particle is the motion equation of an electromagnetic wave in a Schwarzschild metric background. It follows that a particle wave possesses the same physical reality as a classical electromagnetic wave. This last result and the fact that the particle velocity is the group velocity of its wave are in accordance with the opinions of de Broglie and of Schrödinger. We extend these results to the particle subjected to any static field of forces in any gravitational metric background. Therefore we have achieved a synthesis of undulatory mechanics, classical electromagnetism, and gravitation for the case where the field of forces and the gravitational metric background are static, and this synthesis is based only on special and general relativity.     

Spherical gravitational collapse with photon emission and a generalized Schwarzchild interior solution

The general dynamical equations for perfect fluid filled spheres with an outward flux of photons are derived. The vital role played by the energy density of the free gravitational field in accelerating photon production has been emphasized. It is pointed out that even when the material energy density is finite, the energy density of the free gravitational field can take infinitely large values resulting in vanishing surface area of the star. A generalized Schwarzschild interior solution with conformally flat geometry but with photon emission has been obtained. It is pointed out that the interior conformal coordinate system bears a strong resemblance to the exterior Krushkal coordinates. It is shown that for spherical star the invariant velocity of the fluid particles, falling towards the centre, is proportional to its radius suggesting that the outer envelopes collapse at a faster rate than the core part. It is shown that the interior radiating solution can be matched with generalized Schwarzchild exterior solution.     

Equation of Motion of a Mass Point in Gravitational Field and Classical Tests of Gauge Theory of Gravity

A systematic method is developed to study the classical motion of a mass point in gravitational gauge field.First,by using Mathematica,a spherical symmetric solution of the field equation of gravitational gauge field is obtained,which is just the traditional Schwarzschild solution.Combining the principle of gauge covariance and Newton's second law of motion,the equation of motion of a mass point in gravitational field is deduced.Based on the spherical symmetric solution of the field equation and the equation of motion of a mass point in gravitational field,we can discuss classical tests of gauge theory of gravity,including the deflection of light by the sun,the precession of the perihelia of the orbits of the inner planets and the time delay of radar echoes passing the sun.It is found that the theoretical predictions of these classical tests given by gauge theory of gravity are completely the same as those given by general relativity.     

SPHERICALLY SYMMETRIC AND STATIC FIELDS IN LINEARIZED GAUGE THEORIES OF GRAVITATION

In this paper Newtonian limit in the Poincare gauge field theory of gravitation is investigated. In spherically symmetric and static cases interior and exterior solutions of the linearized field equations with gravitational sourtion are obtained by maens of Green's function for the five Lagrangians with out ghosts and tachyons. In cases of four Lagrangians,the space-time metrics outside gravitational source are the usual Schwarzschild one of the first-older, while in the case of the fifth hagrangian the space-time metric differs from the Schwarzschild one. Under both,Newtonian and-weak gravitational field approximations,the motion of a test particle without span should therefore be different from Newton's second law. As a result of the exchanged particles of spin o⁺ the deviation from Newton's second law is a Yukawa term which is attractive. A distance-dependent gravitational "constant" G(r) can be defined according to the new result. The difference between G(r) and Newton's gravitational constant G_∞ is due to a nonzero component of torsion tensor, the effect of which can be tested by measuring G(r).     

A new algorithm for anisotropic solutions

We establish a new algorithm that generates a new solution to the Einstein field equations, with an anisotropic matter distribution, from a seed isotropic solution. The new solution is expressed in terms of integrals of an isotropic gravitational potential; and the integration can be completed exactly for particular isotropic seed metrics. A good feature of our approach is that the anisotropic solutions necessarily have an isotropic limit. We find two examples of anisotropic solutions which generalise the isothermal sphere and the Schwarzschild interior sphere. Both examples are expressed in closed form involving elementary functions only.     

Space-times containing perfect fluids and having a vanishing conformal divergence

The solutions of the Einstein field equations are studied under the assumptions that (1) the source of the gravitational field is a perfect fluid, (2) the divergence of the conformal (Weyl) tensor vanishes, and (3a) either an equation of state exists such thatp=p (w),p being the pressure andw the rest energy density, or (3b) the rest particle density is conserved. Under assumptions (1), (2), and (3a) it is shown that the space-time is conformally flat and the metric is a Robertson-Walker metric. The flow is irrotational, shear-free, and geodesic. Under assumptions (1), (2), and (3b) it is shown that either the line element is static or the fluid has a very special caloric equation of state. Conditions for a static solution to exist are examined, and it is shown that the Schwarzschild interior solution satisfies these conditions as does the Einstein universe. The Schwarzschild interior and the Einstein universe are the only conformally flat, static solutions obeying (1), (2), and (3b).The research reported herein was supported in part by the Atomic Energy Commission under contract number AT (11-1)-34, Project Agreement No. 125.     

Point massive particle in General Relativity

It is well known that the Schwarzschild solution describes the gravitational field outside compact spherically symmetric mass distribution in General Relativity. In particular, it describes the gravitational field outside a point particle. Nevertheless, what is the exact solution of Einstein’s equations with $\delta $ δ -type source corresponding to a point particle is not known. In the present paper, we prove that the Schwarzschild solution in isotropic coordinates is the asymptotically flat static spherically symmetric solution of Einstein’s equations with $\delta $ δ -type energy-momentum tensor corresponding to a point particle. Solution of Einstein’s equations is understood in the generalized sense after integration with a test function. Metric components are locally integrable functions for which nonlinear Einstein’s equations are mathematically defined. The Schwarzschild solution in isotropic coordinates is locally isometric to the Schwarzschild solution in Schwarzschild coordinates but differs essentially globally. It is topologically trivial neglecting the world line of a point particle. Gravity attraction at large distances is replaced by repulsion at the particle neighborhood.     

Surface layers in general relativity and their relation to surface tensions

For a thin shell, the intrinsic 3-pressure will be shown to be analogous to -A, whereA is the classical surface tension: First, interior and exterior Schwarzschild solutions will be matched together such that the surface layer generated at the common boundary has no gravitational mass; then its intrinsic 3-pressure represents a surface tension fulfilling Kelvin's relation between mean curvature and pressure difference in the Newtonian limit. Second, after a suitable definition of mean curvature, the general relativistic analog to Kelvin's relation will be proven to be contained in the equation of motion of the surface layer.     

Spherically symmetric solution in higher-dimensional teleparallel equivalent of general relativity

A theory of(N+1)-dimensional gravity is developed on the basis of the teleparallel equivalent of general relativity(TEGR).The fundamental gravitational field variables are the(N+1)-dimensional vector fields,defined globally on a manifold M,and the gravitational field is attributed to the torsion.The form of Lagrangian density is quadratic in torsion tensor.We then give an exact five-dimensional spherically symmetric solution(Schwarzschild(4+1)-dimensions).Finally,we calculate energy and spatial momentum using gravitational energy-momentum tensor and superpotential 2-form.     

The variant of post-Newtonian mechanics with generalized fractional derivatives

In this article, we investigate mathematically the variant of post-Newtonian mechanics using generalized fractional derivatives. The relativistic-covariant generalization of the classical equations for gravitational field is studied. The equations (i) match the weak Newtonian limit on the moderate scales and (ii) deliver a potential higher than Newtonian on certain large-distance characteristic scales. The perturbation of the gravitational field results in the tiny secular perihelion shift and exhibits some unusual effects on large scales. The general representation of the solution for the fractional wave equation is given in the form of retarded potentials. The solutions for the Riesz wave equation and classical wave equation are clearly distinctive in an important sense. The hypothetical gravitational Riesz wave demonstrates the space diffusion of the wave at the scales of metric constant. The diffusion leads to the blur of the peak and disruption of the sharp wave front. This contrasts with the solution of the D'Alembert classical wave equation, which obeys the Huygens principle and does not diffuse.     

Scattering of particles by deformed non-rotating black holes

We study the excitation of axial quasi-normal modes of deformed non-rotating black holes by test particles and we compare the associated gravitational wave signal with that expected in general relativity from a Schwarzschild black hole. Deviations from standard predictions are quantified by an effective deformation parameter, which takes into account deviations from both the Schwarzschild metric and the Einstein equations. We show that, at least in the case of non-rotating black holes, it is possible to test the metric around the compact object, in the sense that the measurement of the gravitational wave spectrum can constrain possible deviations from the Schwarzschild solution.     

均匀密度零压星的完整的引力解

证明了Oppenheimer和Snyder关于均匀密度零压星的引力塌缩的经典解是不完整的,它并不能正确地连接作为内解和外解的Friedmann度规和Schwarzschild度规;通过在离散时空上拓展解参数而构成了一个完整的引力解,它实现了Friedmann度规和Schwarzschild度规之间的等价连接,并可以证明是奇性自由的;这个完整的引力解显示了物质,引力和离散时空结构之间的关联性 关键词： 均匀密度零压星 Friedmann度规 Schwarzschild度规 离散时空     

Robinson-Trautman equations and Chandrasekhar's special perturbation of the Schwarzschild metric

A perturbation wave solution of the Robinson-Trautman equations is proved to be a perturbation of the Schwarzschild black hole which describes an outgoing axial gravitational wave and corresponds to a special case of Chandrasekhar's algebraically special perturbation of the Schwarzschild metric.     

Pair production by gravitational waves in the field of a black hole

We consider the production of scalar particles by a gravitational wave incident on the static gravitational field of a Schwarzschild mini black hole.     

Extracting the Maxwell charge from the Wheeler–DeWitt equation

We consider the Wheeler–DeWitt equation as a device for finding eigenvalues of a Sturm–Liouville problem. In particular, we will focus our attention on the electric (magnetic) Maxwell charge. In this context, we interpret the Maxwell charge as an eigenvalue of the Wheeler–De Witt equation generated by the gravitational field fluctuations. A variational approach with Gaussian trial wave functionals is used as a method to study the existence of such an eigenvalue. We restrict the analysis to the graviton sector of the perturbation. We approximate the equation to one loop in a Schwarzschild background and a zeta function regularization is involved to handle with divergences. The regularization is closely related to the subtraction procedure appearing in the computation of Casimir energy in a curved background. A renormalization procedure is introduced to remove the infinities together with a renormalization group equation.     

A charged generalization of Florides' interior Schwarzschild solution

The new class of interior Schwarzschild solutions found by Florides is generalized to the charged case. A particular solution within this class is found, which represents an electromagnetic mass-model of a neutral spherically symmetric system. The pressure is isotropic, decreasing monotonously with increasing radius and vanishes at the surface of the matter distribution. The solution is regular everywhere inside a radiusR, and is joined continuously to the exterior Schwarzschild solution at this radius.     

Electrostatic self-force and material sources of the gravitational field

Using a multipolar expansion we determine the electrostatic potential generated by a point source held fixed in the Schwarzschild metric matched successively with two interior metrics, which describes, respectively, two forms of material distributions. The expression of the potential obtained is reformulated by means of the Copson-Linet potential, valid for the Schwarzschild black hole situation. The self-force acting on the source is then determined. We establish that its expression depends on the material sources of the gravitational field. The transition to the black hole situation is then performed.     

Ultrarelativistic black-hole encounters

A method is given for investigating the ultrarelativistic encounter of two black holes which complements the usual low-speed approximation. It depends on the fact that the ultrarelativistic limit of a moving Schwarzschild black hole is a certain plane-fronted impulsive gravitational wave. This enables linearized theory on a curved background to be used. The solution is obtained, with the help of generalized function techniques, to the first order in the background energy, and the radiation pattern at conformal null infinity is examined. The whole approach has a strong connection with the theory of twistors.