https://doi.org/10.1140/epjc/s10052-020-7948-0
Regular Article - Theoretical Physics
Einstein clusters as models of inhomogeneous spacetimes
1
Astronomical Observatory, Jagiellonian University, Kraków, Poland
2
Institute of Physics, Jagiellonian University, Kraków, Poland
3
Copernicus Center for Interdisciplinary Studies, Kraków, Poland
* e-mail: sebastian.szybka@uj.edu.pl
Received:
8
January
2020
Accepted:
17
April
2020
Published online:
11
May
2020
We study the effect of small-scale inhomogeneities for Einstein clusters. We construct a spherically symmetric static 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.
© The Author(s), 2020
