No abstract

The authors consider general methods to solve the equations for Kaluza-Klein cosmological models by using the formal identity of these equations with those of a relativistic point particle in a scalar field. The formal scalar field is given by the phenomenological matter content of the cosmological model in dependence of the difference expansion factors. They find general solutions for one- and two-component matter and general properties of such models.

The Lya forest absorption lines in the spectra of quasars are interpreted as caused by the crossings of the light beam with the walls of a bubble structure (expanding with the Hubble flow only). Then, the typical separation between the absorption lines is proportional to the mean size of the bubbles. The variable factor is the expansion rate H [ z ] . T h e Friedmann regression analysis of the observed line separations determines the density parameter 0 0 and the normalized cosmological term A0 = A c 2 / 3 H i of the appropriate cosmological model: 00 = 0.014 f 0.002, Xo = 1:OSO f 0.006.Depending on the Hubble parameter this method reveals the values of the present mean matter density p~, o = 2.6 h Z . kg m-' and of the cosmological constant A = 3.77 hZ m-' (with h = Ho/(100 km/sMpc)). According to our analysis all models with A = 0 must be excluded. The curvature of space is positive. The curvature radius Ro is 3.3 times the Hubble radius ( c / H o ) . The age t o is 2.8 t,imes the Hubble age (IT;'). A A A subject classification: 161Recently, Hoell and Priester (1991b) ([HP91] hereafter) showed that the Lycr forest in quasar spectra can be understood as the result of a homogeneous bubble structure at least up to a redshift of z = 4.4 if the universe is represented by a Friedmann-Lemaitre model with an actual expansion rate Ho = 90 km/(s.Mpc) and an age of about 30. lo9 years. In the present paper we include data from further spectra, partly new, partly omitted in the first paper because of a too cautious estimation of their sensitivity. The analysis is now based on published spectra of 21 quasars with a total of 1320 Lya absorption lines and supports our former result (Liebscher, Priester, Hoell (1992) ([LPH92] hereafter)). The apparent increase in scatter is balanced by the increase in number. Hence, the estimated variance of the parameters does not change appreciably. The Friedmann regression analysis yields the values of the density parameter Q , and of the normalized cosmological term A 0 = A c 2 / 3 H i . The generalized density parameter Of = Qo + A0 turns out to exceed 1, i.e. the space is closed and the curvature index is k = $1.The method is based on the assumption that the bubble structure in the large scale distribution of matter, which is observed in our galactic neighbourhood up to a redshift of 0.05 (deLapparent et al. 1986) was at rest in comoving coordinates at least since the emission of the quasar light, and that the L y a forest in the quasar spectra is due to the cuts of the light beam through hydrogen filaments within the walls of the bubble structure. For a homogeneous and comoving bubble structure the size parameter X of the voids is independent of time. The mean spacing 2 between the absorption lines is measured as a function of the redshift z itself, and we replace the time t by the corresponding value of the redshift z . If we denote the typical bubble size in comoving radial distance x by X = Ax and the corresponding spacing of the redshifts by 2 = Az, we obtain I8 Astron. Nachr. 313 ...

We analyse the Schwarzschild solution in the context of the historical development of its present use, and explain the invariant definition of the Schwarzschild's radius as a singular surface, that can be applied to the Kerr-Newman solution too.

When sources are added at their right-hand sides, and g (ik) is a priori assumed to be the metric, the equations of Einstein's Hermitian theory of relativity were shown to allow for an exact solution that describes the general electrostatic field of n point charges. Moreover, the injunction of spherical symmetry of g (ik) in the infinitesimal neighbourhood of each of the charges was proved to yield the equilibrium conditions of the n charges in keeping with ordinary electrostatics. The tensor g (ik) , however, cannot be the metric of the theory, since it enters neither the eikonal equation nor the equation of motion of uncharged test particles. A physically correct metric that rules both the behaviour of wave fronts and of uncharged matter is the one indicated by Hély.In the present paper it is shown how the electrostatic solution predicts the structure of the n charged particles and their mutual positions of electrostatic equilibrium when Hély's physically correct metric is adopted.