Einstein clusters as models of inhomogeneous spacetimes
  We study the effect of small-scale inhomogeneities for Einstein clusters. We
construct a spherically symmetric stationary spacetime with small-scale radial
inhomogeneities and propose the Gedankenexperiment. An hypothetical observer at
the center constructs, using limited observational knowledge, a simplified
homogeneous model of the configuration. An idealization introduces side
effects. The inhomogeneous spacetime and the effective homogeneous spacetime
are given by simple solutions to Einstein equations. They provide a basic
toy-model for studies of the effect of small-scale inhomogeneities in general
relativity. We show that within our highly inhomogeneous model the effect of
small-scale inhomogeneities remains small for a central observer. The
homogeneous model fits very well to all hypothetical observations as long as
their precision is not high enough to reveal a tension.
