Up to now we have been considering mainly vacuum spacetimes. Although this has been useful to understand the dynamics of Einstein equations, most of the realistic scenarios involve some kind of matter. For instance, at large scales we have cosmological models, based on the isotropic distribution of dust (i.e., non-interacting particles). At intermediate scales there are galaxy models for dark matter, which has been modeled by using either dust or scalar fields. A small-scale approach would include all types of astrophysical compact objects and the dynamics related to them; binary star evolution, core collapse, accretion disks, etc.
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Bona, C., Bona-Casas, C., Palenzuela-Luque, C. (2009). Matter Spacetimes. In: Elements of Numerical Relativity and Relativistic Hydrodynamics. Lecture Notes in Physics, vol 783. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01164-1_7
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