Pair of null gravitating shells I. Space of solutions and its symmetries

Abstract

The dynamical system constituted by two spherically symmetric thin shells and their own gravitational field is studied. The shells can be distinguished from each other, and they can intersect. At each intersection, they exchange energy on the Dray, 't Hooft and Redmount formula. There are bound states: if the shells intersect, one, or both, external shells can be bound in the field of internal shells. The space of all solutions to classical dynamical equations has six components; each has the trivial topology but a non trivial boundary. Points within each component are labeled by four parameters. Three of the parameters determine the geometry of the corresponding solution spacetime and shell trajectories and the fourth describes the position of the system with respect to an observer frame. An account of symmetries associated with spacetime diffeomorphisms is given. The group is generated by an infinitesimal time shift, an infinitesimal dilatation and a time reversal.

28 pages, 9 figure included in the text, Latex file using amstex, epic and graphic

References in corpus (2)

• Unitary dynamics of spherical null gravitating shells
• Covariant gauge fixing and Kuchar decomposition

Cited by in corpus (8)

• Quantum superposition principle and gravitational collapse: Scattering times for spherical shells
• Quantization of Midisuperspace Models
• Canonical theory of spherically symmetric spacetimes with cross-streaming null dusts
• Reduced Hamiltonian for intersecting shells
• Pair of null gravitating shells II. Canonical theory and embedding variables
• Pair of null gravitating shells III. Algebra of Dirac's observables
• Geometry of crossing null shells
• Dynamics of a self gravitating light-like matter shell with spherical symmetry