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In this paper, we perform a detailed investigation on the various geometricalproperties of trapped surfaces and the boundaries of trapped region in generalrelativity. This treatment extends earlier work on LRS II spacetimes to ageneral 4 dimensional spacetime manifold. Using a semi-tetrad covariantformalism, that provides a set of geometrical and matter variables, wetransparently demonstrate the evolution of the trapped region and also extendHawking's topology theorem to a wider class of spacetimes. In addition, weperform a stability analysis for the apparent horizons in this formalism,encompassing earlier works on this subject. As examples, we consider thestability of MOTS of the Schwarzschild geometry and Oppenheimer-Snydercollapse.

Geometrical properties of trapped surfaces and apparent horizons