Trapped surfaces in quasi-polar gauge

We continue the investigation of the formation of trapped surfaces in strongly curved, conformally flat geometries. Initial data in quasi-polar gauges, rather than in maximal ones, are considered. This implies that apparent horizons coincide with minimal surfaces. Necessary and sufficient conditions for the formation of trapped surfaces are given. These results can be generalized to include the case with gravitational radiation. We have found that the mass of a body inside a fixed volume is bounded from above if the geometry of a Cauchy slice is smooth.