耗散系统不可逆过程中的可拓展广义相对论引力关系

Gravitational relation of prolongable general relativity in the irreversible process of a dissipative system

利用密度分布的不均匀度h(ρ)和粗粒熵S(ρtε)及推导的多标度因数 η 计算式 ,将Weyl曲率拓展为多标度曲率R ;利用与物理量在几何上的奇异性分布有关的多重分形 ,初步建立嵌入Riemann空间的生长结构多重分形几何 ;在此基础上 ,通过引入与分形维数、信息维数和关联维数有关的广义维数Du,建立非保守引力场方程 .分析表明 :新结果为解决宇宙学奇性、星系团的“不明物质”、黑洞的信息疑难。

The heterogeneity h(rho(t))and coarse-grained entropy S(p(epsilon)(t))of the density distribution pin phase space and the derived computational expression of multiscale factor eta* are used in the expansion of Weyl curvature into multiscaled curvature R*; and the multifractal in relation to the singular distribution of physical quantities on geometry is used in the preliminary establishment of the multifractal geometry of growing structures set in Riemann space; on this basis, the equation of non-conservative attractive field is set up by the introduction of the general dimension D-u in relation to the fractal and informational and incident dimensions. The analysis here shows that the new result could render the suitable basis for the settlement of the questions such as the singularity of cosmology the unidentified matter in the cluster of galaxies, the doubt of information from black hole and the unification between gravitation theory and quantum physics, and so on.