NDLI: On a Stationary Cosmology in the Sense of Einstein's Theory of Gravitation

Content Provider	Springer Nature Link
Author	Lanczos, Kornel
Copyright Year	1997
Abstract	A world is to be considered stationary in the sense of general relativity if the coefficients of its metric are independent of time in a coordinate system in which the masses are at rest on average. The remark on the system of coordinates is important because time itself is no invariant notion but is taken only in the sense of proper time. Our definition is unique, in the form given above. On the other hand it is also possible to have points where no matter is present. At such points we may place a test body of infinitesimally small mass and analyse whether it remains at rest in our coordinate system. A necessary and sufficient condition for this is that the time lines of our coordinate system are geodesics. Therefore the static solution given by de Sitter is not an example of a stationary world. The Schwarzschild line element which, from a cosmological point of view, is a world with a single central body can also not be considered a stationary solution. Indeed, there are no stationary solutions which are also spherically symmetric for the original field equations. The only such solution for the cosmological equations is Einstein's cylinder world. It is, to my knowledge, the only stationary world known so far. In that case the average matter density and the total mass of the world has to have a well defined value given by the cosmological constant which doubtless would be purely coincidental and is thus not a satisfactory assumption. In the following we shall discuss a new solution which is in accord with the original field equations without the need of an a priori relation between mass and cosmological constant. However, we shall find that its mass cannot be less than the mass of the cylinder world.
Starting Page	363
Ending Page	399
Page Count	37
File Format	PDF
ISSN	00017701
Journal	General Relativity and Gravitation
Volume Number	29
Issue Number	3
e-ISSN	15729532
Language	English
Publisher	Kluwer Academic Publishers-Plenum Publishers
Publisher Date	1997-01-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Differential Geometry Mathematical and Computational Physics Relativity and Cosmology
Content Type	Text
Resource Type	Article
Subject	Physics and Astronomy

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