LONG-WAVELENGTH ITERATION OF EINSTEINS EQUATIONS NEAR A SPACETIME SINGULARITY

We analyze the behavior of a very inhomogeneous spacetime near the sin gularity by using the recently developed long wavelength iteration sch eme of Einstein's equations. Near the singularity, the local anisotrop y cannot be neglected and we give the first order and third order solu tions for any perfect fluid adiabatic index. We also clarify the links between a recently developed long wavelength iteration scheme of Eins tein's equations, the Belinski-Khalatnikov-Lifschitz (BKL) general sol ution near a singularity, and the anti-Newtonian scheme of Tomita. We determine the regimes when the long wavelength or anti-Newtonian schem e is directly applicable and show how it can otherwise be implemented to yield the BKL oscillatory approach to a spacetime singularity.