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 R_{max}(Λ)>>r>>R_{min}(Λ), within which the Newtonian limit is valid. It also leads to the existence of a maximum mass, M_{max}(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:

International Journal of Modern Physics D
 Pub Date:
 2001
 DOI:
 10.1142/S0218271801001189
 arXiv:
 arXiv:grqc/0004037
 Bibcode:
 2001IJMPD..10..649N
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 Latex, 15 pages, no figures, errors corrected