GT6 - Exact Solutions (mathematical aspects) |
Speaker_ |
Baranov, Alexandre |
Talk _ |
ON STRATIFORM STRUCTURE'S MODEL OF OPEN UNIVERSE |
Abstract _ |
The open Universe model is described by the conformally flat 4D metric $ds^2 = exp(2\sigma(S))\cdot \delta_{\mu\nu}dx^{\mu}dx^{\nu}$ with $S^2 = t^2-r^2$ ($t, r$ are time and radial variables); $\delta_{\mu\nu}= diag(1,-1,-1,-1).$ Einstein's equations are separated into two equations: for an energy density $\varepsilon(S)$ and a pressure $p(S).$ A relation $p/\varepsilon = \beta(S)$ is introduced. A function of state $\beta(S)$ as a quasistairs function $\beta(S)= (a/S-sin(a/S))/b$ is taken. Constants $a,$ $b$ are connected with the number of steps and values of $\beta$ ($|\beta(S)| \leq 1$). When $S \rightarrow \infty$ than $\beta=0$ (Friedman's solution). A function $\beta_1(S)$ is a fuzzy step-function for one step. In this case $\sigma(S)$ may be written as a quadrature. |