Imbedding a Schwarzschild mass into cosmology

Document Type

Article

Publication Date

1-1-1984

Abstract

We develop a method for imbedding a Schwarzschild mass into a zero-curvature universe. We work with curvature coordinates (R,T), in terms of which the metric has the form ds2(R,T)=A-1(R,T)dR2+R2d2-B(R,T)dT2, and coordinates (R,), 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 Rb. Inside Rb 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. © 1984 The American Physical Society.

Identifier

0000368456 (Scopus)

Publication Title

Physical Review D

External Full Text Location

https://doi.org/10.1103/PhysRevD.29.198

ISSN

05562821

First Page

198

Last Page

206

Issue

2

Volume

29

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