Gravitational collapse of spherical clouds and formation of black holes in the background of dark energy.
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In this thesis, I first review the fundamentals of Einstein's theory of gravity in four-dimensional spacetimes, and then develop the general formulas of thin shells in this theory. Applying these formulas to spherically symmetric thin shells, I study the gravitational collapse of dust clouds in the background of dark energy. To solve the relevant equations, I develop a computer program, and investigate four representative cases, in which one is without dark energy and the others are with. I find that in all the four cases black holes can be formed from the gravitational collapse of the dust cloud.