I understand that in general relativity, we describe the universe by the relationship between objects "in it". I quote "in it" because in this model, there is no background where the objects exist.
How does GR describes a universe with only one object and nothing more? what about a universe where only two objects exist?
Is it possible to describe universes made of a few bodies?
I understand that in general relativity, we describe the universe by the relationship between objects "in it".
This is not true. This is more like what Einstein hoped his theory would be like, and how he depicted his interpretation of it in his 1916 paper, "The foundation of the general theory of relativity."
The reality is that GR doesn't really embody Mach's principle to any great extent. For example, GR allows us to have a universe in which the only dynamical phenomena are gravitational waves, which interact with each other. Such a universe is complex and interesting, and GR predicts things about it, e.g., the fact that the waves are transverse, and fact that they can interact to form black holes.
