Theoretical determination of the thinning factor in relativistic hierarchical cosmology

Recent computer simulations by Haggerty (1974) and Janin (1974) on the gravitational clumping of bodies into clusters and superclusters in Newtonian cosmology have given an approximate value of theta=1.9 for the thinning factor (defined for two systems of sizes R1, R2 and densities rho1, rho2 by rho1/rho2= (R2/R1)sup(theta)), close to the observed value of theta = 1.7. To get an almost exact value of theta in a general relativistic hierarchy, algebraic conditions on the metric tensor are employed: the result is theta=2, with the hierarchy characterized by a dimensionless constant of value approximately 2 x 10-7. A condition of systems is also found for objects of sufficiently high angular momentum. (Auth.)