MECHANISM OF TRAPPED SURFACE FORMATION

By a combination of analytical and numerical methods, the density prof ile of a spherical star momentarily at rest is varied, and the corresp onding response in the area of the spherical shells is monitored. it i s shown that the inner apparent horizon (if it exists) must lie within or at most on the star's surface while no such restriction is found f or the outer apparent horizon. An apparent horizon, however, lying in the vacuum region will always have a nonvanishing area, as long as the ADM mass of the system is nonzero. Furthermore for density profiles n ot decreasing outwards, it appears that all spherical trapped surfaces lie on a thick spherical shell. Finally for a uniform density star a simple criterion is found, relating the density and proper radius that guarantees the presence or absence of trapped regions.