I read many articles about space-times. Most authors consider these spaces as warped product manifolds $I\times M$ where $I$ is an open connected interval of the real line and $M$ is a Riemannian manifold. Minkowski space-time, anti-de Sitter, and the Einstein static universe are well-known examples of such space-times. Many authors considered a general metric of these three examples and construct the so-called static space -times.
My question is: Is there a generalized metric on all space-times?
Note that my question is not about the most generalized metric but about the generalized metric of the existing ones.
I want to bank up the existing metrics in one generalized metric. One may consider for example $I\times S^n$.
Thanks in advance