Motion of Isolated bodies

TL;DR

This paper demonstrates that smooth initial data for Einstein-dust and Einstein-Maxwell-dust equations evolve into solutions depicting isolated bodies with matter confined to a finite region surrounded by vacuum.

Contribution

It establishes conditions under which solutions to Einstein-dust and Einstein-Maxwell-dust equations form isolated bodies with matter confined spatially.

Findings

Matter remains spatially compact over time.

Solutions include an exterior vacuum region.

Initial data evolve into isolated body configurations.

Abstract

It is shown that sufficiently smooth initial data for the Einstein-dust or the Einstein-Maxwell-dust equations with non-negative density of compact support develop into solutions representing isolated bodies in the sense that the matter field has spatially compact support and is embedded in an exterior vacuum solution.