天体物理非线性问题初探-活动星系核的光变及引力的局部近似

展示活动星系核研究和引力研究中的一些难点，揭示了某些天体的光变存在分形结构的可能性。我们提出了活动星系核的中心黑洞具有某种随机微活动性的假设，该假设可解释活动星系核的一些观测现象。我们发现Ｗｅｉｅｒｓｔｒａｓ函数的分形图形可以用来很好地拟合ＯＪ２８７的短时标光变。一个用Ｗｅｉｅｒｓｔｒａｓ函数构造的分形曲线与ＯＪ２８７的历史光变的线性相关系数达到了０．７３。我们计算了ＯＪ２８７光变曲线的计盒维数，信息维数和关联维数，结果表明，这些维数均大于１。我们研究了两个活动星系核（ＯＪ２８７和３Ｃ３４５）的历史光变，发现在星等和这两个物体滞留在这个星等之下的时间长度的对数之间存在线性关系。这种关系可能源于光变的分形结构。我们提出，空时点及附于该点的一个标架与Ｍｉｎｋｏｗｓｋｉ空间上的一个３阶反对称张量场对应。场中的张量取自于一个固定的张量集合。我们得到了Ｒｉｅｍａｎｎ正则坐标下引力场的一个级数表示式。我们还计算了Ｒｉｃｃｉ张量的线性近似和一级非线性近似。这有利于强引力场下的局部非线性结构分析。期望对于引力的进一步研究，通过非线性科学这门新方法的桥粱，沟通极端天文现象与基本引力相互作用之间的鸿沟

Study on Nonlinear Problems in Astrophysics-Light Variabilityof Active Galactic Nuclei and Local Approximation of Gravity

This presentation displays some difficulties in research on Active Galactic Nuclei and Gravitation, and reveals evidences of fractal structure in light curves of some objects. It is assumed that the center black holes of Active Galactic Nuclei possess some stochastic microvariability which gives explanation of some observational results. It is found that the Weierstrass function may be used to imitate the short time scale variability of OJ287. A fractal curve constructed by the function possesses a correlation coefficient(0.73)to the light curve. The capacity-dimension, information-dimension and correlation-dimension of the light curve are also calculated. The calculations indicate that their values are more than 1. The historical light curves of two Active Galactic Nuclei(AGNs): OJ287 and 3C345 are also studied. The linear dependence has been found between the magnitude and the logarithm of the length of the time. The relation may originate from a fractal structure of the light curve. A space-time point with a frame is proposed to be related to a skew-symmetric tensor field of degree 3 defined on Minkowski space. A series expression of metric in Riemannian normal coordinates is obtained which is based on the proposition. The linear and first order nonlinear approximations of Ricci tensor, which may be favorable to the local analysis of strong gravity is also presented. With further study of gravitation it is expected that gap between extreme astronomical phenomena and elementary gravitational interaction will be even out by the nonlinear scientific methods.