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

TL;DR

This paper analyzes the classical solutions of a system of two spherically symmetric gravitating shells, exploring their dynamics, intersections, and symmetries, revealing a complex solution space with six components and specific symmetry groups.

Contribution

It provides a detailed characterization of the solution space, including its topology, parameters, and symmetries, for two intersecting gravitating shells in general relativity.

Findings

Six components in the solution space with non-trivial boundaries

Solutions characterized by four parameters including geometry and observer position

Symmetry group generated by time shift, dilatation, and time reversal

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.