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Gravitational collapse in loop quantum gravity. (English) Zbl 1140.83354

Summary: In this paper we study the gravitational collapse applying methods of loop quantum gravity to a minisuperspace model. We consider the space-time region inside the Schwarzschild black hole event horizon and we divide this region in two parts, the first one where the matter (dust matter) is localized and the other (outside) where the metric is Kantowski-Sachs type. We study the Hamiltonian constraint obtaining a set of three difference equations that give a regular and natural evolution beyond the classical singularity point in “\(r=0\)” localized.

MSC:

83C45 Quantization of the gravitational field
83C75 Space-time singularities, cosmic censorship, etc.
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