Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1996-08-21
J.Math.Phys. 37 (1996) 6293-6301
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
18 pages, LaTex file, no figures, to appear in the J. Math. Phys
Scientific paper
10.1063/1.531777
We calculate the total gravitational energy and the gravitational energy density of the de Sitter space using the definition of localized energy that arises in the framework of the teleparallel equivalent of general relativity. We find that the gravitational energy can only be defined within the cosmological horizon and is largely concentrated in regions far from the center of spherical symmetry, i.e., in the vicinity of the maximal spacelike radial coordinate $R=\sqrt{ 3 \over \Lambda}$. The smaller the cosmological constant, the farther the concentration of energy. This result complies with the phenomenological features of the de Sitter space, namely, the existence of a radial acceleration directed away from the center of symmetry experienced by a test particle in the de Sitter space. Einstein already contemplated the de Sitter solution as a world with a surface distribution of matter, a picture that is in agreement with the present analysis.
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