Exact Vacuum Solutions to the Einstein Equation
01 Jan 2007-Vol. 28, Iss: 5, pp 499-506
TL;DR: In this paper, Laplace et al. describe Laplace 2D Laplace and Laplace Laplace 3D 2D 2-dimensional Laplace, a 2D 3-dimensional 2D model.
Abstract: 在这篇论文，作者为得到一系列准确真空答案到爱因斯坦方程介绍一个框架。分辨率的这个过程基于度量标准的一种正规形式。根据这个过程，爱因斯坦方程能被归结为一些 2-dimensional 象 Laplace 一样方程或旋转；分叉方程，它对决定方便。
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TL;DR: In this paper, the system of Friedman-Robertson-Walker (FRW) metric coupling with massive nonlinear dark spinors was discussed in detail, where the thermodynamic movement of spinors is also taken into account.
Abstract: In this paper, we discuss the system of Friedman–Robertson–Walker (FRW) metric coupling with massive nonlinear dark spinors in detail, where the thermodynamic movement of spinors is also taken into account. The results show that, the nonlinear potential of the spinor field can provide a tiny negative pressure, which resists the universe to become singular. The solution is oscillating in time and closed in space, which approximately takes the form: $g_{\mu
u} = \bar R^2(1-\delta\cos t)^2\diag(1,-1,-\sin^2r,-\sin^2r\sin^2\theta)$, with $\bar R = (1\sim 2) \times 10^{12}$ light year, and δ = 0.96 ~ 0.99. The present time is about t ~ 18°.
33 citations
TL;DR: In this paper, a new algorithm was developed to find the exact solutions of the Einstein's field equations, and the singularities of the time-periodic solutions were investigated and some new physical phenomena, such as degenerate event horizon and time periodic event horizon, were found.
Abstract: In this paper, we develop a new algorithm to find the exact solutions of the Einstein’s field equations. Time-periodic solutions are constructed by using the new algorithm. The singularities of the time-periodic solutions are investigated and some new physical phenomena, such as degenerate event horizon and time-periodic event horizon, are found. The applications of these solutions in modern cosmology and general relativity are expected.
17 citations
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TL;DR: In this article, a light-cone coordinate system for a 1+3 dimensional Lorentzian manifold is proposed, which takes a wonderful canonical form, which is much helpful for resolving the Einstein's field equation.
Abstract: If there is a null gradient field in a 1+3 dimensional Lorentzian manifold, we can establish a kind of light-cone coordinate system for the manifold from the null gradient field. In such coordinate system, the metric takes a wonderful canonical form, which is much helpful for resolving the Einstein's field equation. In this paper, we show how to construct the new coordinate system, and then explain their geometrical and physical meanings via examples. In the light-cone coordinate system, the complicated Einstein's field equation could be greatly simplified. This coordinate system might be also helpful to understand the propagation of the gravitational wave.
5 citations
TL;DR: In this article, a framework based on Clifford algebra is proposed to classify elementary fields and derive their dynamical equations and transformation laws in detail, and some new insights into their unusual properties are provided.
Abstract: According to a framework based on Clifford algebra $$C\ell (1,3)$$
, this paper gives a classification for elementary fields, and then derives their dynamical equations and transformation laws in detail. These results provide an outline on elementary fields and some new insights into their unusual properties. All elementary fields exist in pairs, and one part of the pair is a complex field. Some intrinsic symmetries and constraints such as Lorentz gauge condition are automatically included in the canonical equation. Clifford algebra $$C\ell (1,3)$$
is a natural language to describe the world. In this language, the representation formalism of dynamical equation is symmetrical and elegant with no more or less contents. This paper is also a summary of some previous problem-oriented researches. Solutions to some simple equations are given.
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TL;DR: In this paper, the authors derived and simplified the complete dynamical equation system for a collapsing spherically symmetrical star with perfect fluid, and established some new constraints on the initial and boundary conditions.
Abstract: In this paper, we examine the dynamical behavior of a collapsing star via fully dynamical approach. We derive and simplify the complete dynamical equation system for a collapsing spherically symmetrical star with perfect fluid, and establish some new constraints on the initial and boundary conditions. The mass density near the center can be approximately derived in the light-cone coordinate system. The results show that, the singularity can not form at the center if the equation of state satisfies some increasing and causal conditions and the initial distributions of mass-energy density and velocity are suitable. The dynamical equations can even automatically remove the weak singularity in the initial data. The analysis may give some insights into the structure of a star and the nature of the black hole.
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