Collapse Condition for a Spherically Symmetric Static Universe

POSTER

Abstract

A static model of a universe has been obtained from Einstein's equations for a gravitational field inside a sphere of a radius A, filled with a incompressible liquid of a constant density 10$^{-31}$ g/cm$^{3}$. It is shown that gravitational collapse occurs in the scale 11.94x10$^{28}$ cm $<$ R $<$ 12.69x10$^{28}$ cm so that the gravitational radius is R$_{g}\le $A: at the Hubble radius, R$_{H}$=1.3x10$^{28}$ cm, collapse is impossible. Two models are considered: 1) a Hubble universe (A=R$_{H})$; 2) a universe containing a collapsar inside (R$_{g}<$A). Both cases contain a gravitational inertial force of repulsion, which is proportional to distance R. Three-dimensional curvature is negative and constant in the both cases. Four-dimensional curvature is 1) positive always in a Hubble universe (Case 1, A=R$_{H})$, 2) increasing from a negative value on the sphere's radius A, then getting zero value within the sphere up to positive infinity on the collapsar's surface (Case 2, A$>$R$_{g})$. Redshift in both models is due to the repulsing gravitational inertial force (not the Doppler effect), and is a square function of distance at large R.

Authors

  • Dmitri Rabounski

  • Larissa Borissova

    Goi\^ania, Goi\&#039;as, Brazil/ Naturoptics, Goi\^ania, Goi\&#039;as, Brazil, Naturoptics, Goi\^ania, Goi\&#039;as, Brazil, and Naturoptics, Naturoptics/DECEASED, Naturoptics, DECEASED