Classical dynamics and stability of collapsing thick shells of matter.

*(English)*Zbl 1091.83017The authors of the paper study the classical dynamics of a collapsing spherical shell (which the authors call a macroshell) with an inner massive core of greater mass and study the conditions under which the matter composing the shell remains confined around its mean radius. In order to verify this property, the authors discretize the continuous distribution of matter and study the conditions under which the matter composing the shell remains confined around its mean radius. The microshels can be ellectrically charged, as well, as a de Sitter component of the gravitational field could be non zero. The dynamics of the shells is described by means of Israel’s (Lanczos) junction conditions for singular hypersurfaces and adopting a Hartree (mean-field) approach, an effective Hamiltonian for the motion of each microshell is derived which allow them to check the stability of the matter composing the macroshell. The authors end by briefly commenting on the quantum effects which may arise from the extension of their classical treatment to the semiclassical level. The reviewer is founding some analogies with a problem, in which one considers the Hawking’s emission of mass particles on bound levels near a black hole. Under some conditions the accumulation (self-stimulated emission of bosons) of particles could be exponentially fast and could be much faster than the Hawking’s emission of particles to spatial infinity. Then an envelope of particles could form around the Black Hole, which is analogous to the shell, examined in the paper under review.

Reviewer: Alex Gaina (Chisinau)

##### MSC:

83C55 | Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.) |