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230 EXACT SOLUTIONS AND SCALAR FIELDS IN GRAVITY
approaches a rotating steady state in the zooming space. In the ordinary
coordinates, the central core is seen to rotate non-uniformly and
by it starts deforming into an elongated bar as a result of the
growth of a non-axisymmetric instability. Figure 1 displays equatorial
density contours of the central cloud portion at when a
dense bar has already formed. In Ref. [19] it is studied the mechanisms
responsible for bar formation within a collapsing disk using the zooming
coordinates. They found that the growth of the shear component of velocity
may induce a non-uniformly rotating disklike core to elongate into
a barlike configuration. Subsequent collapse of the central bar is seen
to proceed self-similarly. That is, the bar shrinks faster in the direction
of the cylindrical radius than along the long axis. As a consequence the
collapsing bar becomes progressively narrower and a filamentary structure
eventually forms as shown in Figure 2 at At this time, the
density of the filament is and because of the assumption
of isothermality it will undergo undefinite collapse upon itself. This solution
strongly resembles the self-similar solution for isothermal collapse
first found in Ref. [15]. They predicted by linear analysis that when the
mass per unit length of an infinitely long cylinder is much greater than
the equilibrium value fragmentation of the cylinder
will not occur as long as the collapse remains isothermal. The details of