THE SINGULARITY IN GENERIC GRAVITATIONAL COLLAPSE IS SPACELIKE, LOCALAND OSCILLATORY

A longstanding conjecture by Belinskii, Khalatnikov and Lifshitz that the singularity in generic gravitational collapse is spacelike, local and oscillatory is explored analytically and numerically in spatially inhomogeneous cosmological space-times. With a convenient choice of va riables, it can be seen analytically how nonlinear terms in Einstein's equations control the approach to the singularity and cause oscillato ry behavior. The analytic picture requires the drastic assumption that each spatial point evolves toward the singularity as an independent s patially homogeneous universe. In every case, detailed numerical simul ations of the full Einstein evolution equations support this assumptio n.