CHAOS IN THE EINSTEIN EQUATIONS

We discuss some results (and open questions) obtained in connection with a particular toy-model study of a space-time metric evolved under the governing Einstein equations. The toy-model describes a gravitational collapse towards a space-time singularity and illustrates how complicated (unpredictable, chaotic) dynamical behavior of the metric may arise due to the nonlinearity of the Einstein equations. It is noted, that a ''Lyapunov exponent'' (which is a standard diagnostic indicator for chaos) does not suffice as an indicator of chaos in this context, since this measure is highly gauge-dependent. The possibility of constructing a gauge-invariant generalization of a ''Lyapunov exponent'' should be analyzed further. Some remarks concerning a ''toy-application'' of quantum principles to the gravitational collapse are made.