The passage discusses the effects of inhomogeneity on cosmological models, focusing on the behavior of dust particles (nebulae) distributed non-uniformly but with spherical symmetry. The author, Richard C. Tolman, uses a set of co-moving coordinates to derive the line element and its consequences, leading to expressions for the energy-momentum tensor. By solving the resulting equations, Tolman demonstrates that inhomogeneities can lead to instabilities in both static and non-static models, such as the Einstein and Friedmann models. Specifically, disturbances away from uniform distributions can tend to increase over time, and non-interacting zones can behave differently from homogeneous models. Tolman concludes that these findings highlight the limitations of homogeneous models in describing the actual universe, emphasizing the need for caution in making wide extrapolations from homogeneous models to the entire universe. He suggests that regions beyond the range of current telescopes might be contracting rather than expanding and could contain matter with different densities and evolutionary stages.The passage discusses the effects of inhomogeneity on cosmological models, focusing on the behavior of dust particles (nebulae) distributed non-uniformly but with spherical symmetry. The author, Richard C. Tolman, uses a set of co-moving coordinates to derive the line element and its consequences, leading to expressions for the energy-momentum tensor. By solving the resulting equations, Tolman demonstrates that inhomogeneities can lead to instabilities in both static and non-static models, such as the Einstein and Friedmann models. Specifically, disturbances away from uniform distributions can tend to increase over time, and non-interacting zones can behave differently from homogeneous models. Tolman concludes that these findings highlight the limitations of homogeneous models in describing the actual universe, emphasizing the need for caution in making wide extrapolations from homogeneous models to the entire universe. He suggests that regions beyond the range of current telescopes might be contracting rather than expanding and could contain matter with different densities and evolutionary stages.