Mathematics
Scientific paper
Apr 1981
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981ncimb..62..327b&link_type=abstract
Nuovo Cimento B, Serie 11, vol. 62B, Apr. 11, 1981, p. 327-336.
Mathematics
1
Cosmology, Relativity, Space-Time Functions, Tensors, Einstein Equations, Function Space, Manifolds (Mathematics), Universe, Vacuum
Scientific paper
The problem of constructing the metric tensor of empty space corresponding to that in special relativity from the equations of general relativity is examined for the case when the equations of general relativity include a cosmological term. It is shown that the de Sitter universe, representing the solution of the equations of general relativity with the cosmological term in empty space, may be transformed into the Castelnuovo universe, which may be interpreted as the geodesic representation of the pseudo-Riemannian de Sitter manifold on a flat manifold. The Castelnuovo universe is shown to be indistinguishable from the Minkowski universe on distances small in comparison with the radius of the universe, exhibiting straight-line geodesics, light cones, and a metric tensor invariant under Lorentz transformations. Finally, it is noted that in the case of an infinite universe, the de Sitter, Castelnuovo and Minkowski metrics become coincident, a fact which may be interpreted as proving the theorems of Serini, Einstein and Pauli, and Lichnerowitz.
Benza Vincenzo
Caldirola P.
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