The Consistent Newtonian Limit of Einstein's Gravity with a Cosmological Constant

Details The Consistent Newtonian Limit of Einstein's Gravity with a Cosmological Constant The Consistent Newtonian Limit of Einstein's Gravity with a Cosmological Constant

2000-04-12

arxiv.org/abs/gr-qc/0004037v2

Int.J.Mod.Phys. D10 (2001) 649-662

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Latex, 15 pages, no figures, errors corrected

Scientific paper

10.1142/S0218271801001189

We derive the `exact' Newtonian limit of general relativity with a positive cosmological constant $\Lambda$. We point out that in contrast to the case with $\Lambda = 0 $, the presence of a positive $\Lambda$ in Einsteins's equations enforces, via the condition $| \Phi | \ll 1$, on the potential $\Phi$, a range ${\cal R}_{max}(\Lambda) \gg r \gg {\cal R}_{min} (\Lambda)$, within which the Newtonian limit is valid. It also leads to the existence of a maximum mass, ${\cal M}_{max}(\Lambda)$. As a consequence we cannot put the boundary condition for the solution of the Poisson equation at infinity. A boundary condition suitably chosen now at a finite range will then get reflected in the solution of $\Phi$ provided the mass distribution is not spherically symmetric.

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