G. S. Bisnovatyi-Kogan

Models of clusters of point masses with large central redshifts

ConclusionsIn the Newtonian case we have obtained an isotropic self-consistent distribution of gravitationally interacting point masses which satisfies the transport equation without collisions, and the gravitational equation for an arbitrary powerfunction density distribution ρ=βr−s, s<3.For ρ=βr−2 the analogous self-consistent solution was obtained for the anisotropic distribution function both in Newtonian and GTR cases.The GTR solutions with ρ=βr−2 have central redshifts which increase without limit in accordance with the law 1+z∼r−1/α as we approach the center. In the isotropic case, they appear to be stable when the mean velocities are much less than the velocity of light u<0.2c, α>21.The hydrodynamic GTR solution was found for a perfect gas at constant temperature (but variable T′=T(g00)1/2) which also has z→∞ for r→0.We should like to thank K. Thorne, L. Hazin, and M. Podurets for valuable discussions. K. Thorne was particularly helpful in supplying unpublished results on circular orbits obtained by American authors.

Theory of gravitational stability of a rotating cylinder

The stability of a rotating dust cylinder against perturbations located in the plane perpendicular to the axis of rotation is investigated. It is shown that a homogeneous rotating cylinder containing a weak inhomogeneity is stable against such perturbations. A weakly inhomogeneous cylinder with opposite streams of equal density is unstable for thel=2 mode in the case of a perturbation of the form∼ei(lϕ−ωt), when the density increases radially. The instability of a system consisting of a homogeneous rotating dust cylinder in a hot homogeneous medium is determined. It is shown that the maximum growth rate corresponds tol = 2 when the density of a cold cylinder is not negligible in comparison with the density of the medium. In the opposite case, the maximum growth rate shifts toward l=3. An attempt is made to associate the existence of the maximum growth rate for l=2 with the presence of two spiral arms in most galaxies. It is shown that, when the longitudinal temperature is high enough, a rotating cylinder which is bounded in the radial direction is stable against arbitrary perturbations.