Abstract
We develop a method for imbedding a Schwarzschild mass into a zero-curvature universe. We work with curvature coordinates (,), in terms of which the metric has the form , and coordinates (,), where is measured by radially moving geodesic clocks. We solve the field equations for a stress-energy tensor that corresponds to a radially moving perfect geodesic fluid outside some boundary . Inside we take the stress-energy tensor to be composed of a perfect-fluid part and a Schwarzschild matter part. Specific examples of imbedding a mass into a de Sitter universe and a pressure-free Einstein—de Sitter universe are given, and we show how to extend our methods to general zero-curvature universes. A consequence of our results is that there will be spiralling of planetary orbits when a mass such as our Sun is imbedded in a universe. We relate our work to recent work done by Dirac with regard to his Large Numbers hypothesis.
- Received 21 March 1983
DOI:https://doi.org/10.1103/PhysRevD.29.198
©1984 American Physical Society