  Using a scalar field as an intrinsic 'clock' while investigating the dynamics
of gravitational systems has been successfully pursued in various researches on
the border between classical and quantum gravity. The objective of our research
was to check explicitly whether the scalar field can serve as a time variable
during dynamical evolution of the matter-geometry system, especially in regions
of high curvature, which are essential from the perspective of quantum gravity.
For this purpose, we analyzed a gravitational collapse of a self-interacting
scalar field within the framework of general relativity. The obtained results
indicated that the hypersurfaces of constant scalar field are spacelike in
dynamical regions nearby the singularities formed during the investigated
process. The scalar field values change monotonically in the areas, in which
the constancy hypersurfaces are spacelike.
