Mathematics – Logic
Scientific paper
Mar 1997
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997gregr..29..361l&link_type=abstract
General Relativity and Gravitation, Vol. 29, p. 361-399 (1997)
Mathematics
Logic
10
Scientific paper
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 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.
Hoenselaers Cornelius
Lanczos Kornel
No associations
LandOfFree
On a Stationary Cosmology in the Sense of Einstein's Theory of Gravitation [1923] does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On a Stationary Cosmology in the Sense of Einstein's Theory of Gravitation [1923], we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On a Stationary Cosmology in the Sense of Einstein's Theory of Gravitation [1923] will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-1860269