The formation of trapped surfaces in the gravitational collapse of spherically symmetric scalar fields with a positive cosmological constant

Abstract

Given spherically symmetric characteristic initial data for the Einsteinscalar field system with a positive cosmological constant, we provide a criterion, in terms of the dimensionless size and dimensionless renormalized mass content of an annular region of the data, for the formation of a future trapped surface. This corresponds to an extension of Christodoulou's classical criterion by the inclusion of the cosmological term.

Trapped surface formation for spherically symmetric Einstein-Maxwell-charged scalar field system with double null foliation

“…Within the study of spherically symmetric systems, there are interesting results on formation of trapped surfaces and singularities for other matter models, e.g. Einstein-Vlasov studied by Andréasson [6], Andéasson-Rein [7], Moschidis [19], Einstein-Euler studied by Burtscher and LeFloch [8], Einsteinscalar field studied by Li-Liu [17], An-Zhang [4], An-Gajic [5], Einstein-null dust studied by Moschidis [20], Einstein-scalar field with positive cosmological constant by Costa [13]. For the Einstein-Maxwell-(real) scalar field system, we refer interested readers to [14,15] by Dafermos,[18] by Luk and Oh on the recent development of proving strong cosmic censorship.…”