The Consistent Newtonian Limit of Einstein's Gravity with a Cosmological Constant
Abstract
We derive the ``exact'' Newtonian limit of general relativity with a positive cosmological constant Λ. We point out that in contrast to the case with Λ=0, the presence of a positive Λ in Einsteins's equations enforces, via the condition |Φ|<<1 on the potential Φ, a range Rmax(Λ)>>r>>Rmin(Λ), within which the Newtonian limit is valid. It also leads to the existence of a maximum mass, Mmax(Λ). 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 Φ provided the mass distribution is not spherically symmetric.
- Publication:
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International Journal of Modern Physics D
- Pub Date:
- 2001
- DOI:
- 10.1142/S0218271801001189
- arXiv:
- arXiv:gr-qc/0004037
- Bibcode:
- 2001IJMPD..10..649N
- Keywords:
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- General Relativity and Quantum Cosmology
- E-Print:
- Latex, 15 pages, no figures, errors corrected