Singularities in separable metrics with spherical, plane, and hyperbolic symmetry
The authors consider solutions of the Einstein equations for a perfect fluid, with a separable diagonal metric of the form \[ ds\quad 2=-w\quad 2(x)v\quad 2(t)dt\quad 2+g\quad 2(t)S\quad 2(x)dx\quad 2+A\quad 2(t)B\quad 2(x)[dy\quad 2+h\quad 2(y)\quad dz\quad 2]. \] They demand that the fluid obeys both the weak and the strong energy conditions and that the curvature scalar \(R^{abcd} R_{abcd}\) does not become singular on \(x=const\). surfaces. They show that the only non-static solutions are the Robertson-Walker space-times, the space-times with \(w=S=B=1\), and a certain class of plane symmetric solutions.
scientific article; zbMATH DE number 4062110