THE APPEARANCE OF APPARENT HORIZONS AND CUSP SINGULARITY

Some one-parameter families of time-symmetric Cauchy hypersurfaces wer e investigated. All of them have such a property that for some 'critic al' value of the parameter an apparent horizon appears. It turns out t hat for parameter values sufficiently close to the critical one, numer ous properties of the horizon are 'universa' (i.e. independent of deta ils of geometry and distribution of matter). It was conjectured that t he above 'universality' property occurs in the case of typical one-par ameter time-symmetric families of Cauchy hypersurfaces.