Bound systems in an expanding universe

Abstract

The Schwarzchild solution insertion in an expanding universe, the so-called "Swiss cheese model," is shown to possess a very unphysical property. Specifically, in this model some trajectories are discontinuous functions of their initial conditions. An alternate metric is proposed as a remedy. It goes smoothly between the Schwarzchild exterior solution and the Friedmann-Lemaitre, expanding universe metric. It is further shown that the effects of the expansion on planetary motions in the solar system are too small to be currently observed for this alternate metric.

More explanation has been added and an error has been corrected, i.e. the extrinsic curvature is continuous, however some of the trajectories are discontinuous functions of the initial conditions

Cited by in corpus (4)

• Quasi-local masses and cosmological coupling of black holes and mimickers
• On the influence of the global cosmological expansion on the local dynamics in the Solar System
• Turnaround physics beyond spherical symmetry
• Constraining the swiss-cheese IR-fixed point cosmology with cosmic expansion