Analytical solution to the dynamics underlying the Belinski-Khalatnikov-Lifshitz scenario.

An exact solution of the equations underlying the Belinski-Khalatnikov-Lifshitz (BKL) scenario is derived and tested for the stability against small perturbations. The regularity of the dynamics is examined using dynamical systems method. An instability and strong nonlinearity of the dynamics occur in the vicinity of the gravitational singularity. Our results present the properties of spacetime near the generic gravitational singularity and seem to be consistent with the BKL conjecture.