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 Weierst rass function may be used to imitate the short time scale variability of OJ287.A fractal curve const ructed 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 thei rvalues 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-symmet rictensor 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 Riccitensor, 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 beeven out by the nonlinear scientific methods.