Introduction to the Oscillating Spherical Mass Shell

## The Basic Equations

This entire calculation is performed in relativistic scalar gravitation. While scalar gravity is not the correct theory of gravitation, it is conceptally much simpler than general relativity, and it shares many of the characteristic features. The field equation is given by:

Note that the exponential term on the right side of the equation makes the field equation nonlinear. The particle (geodesic) equations of motion are:

## The Setup

An infinitesimally thin, spherical shell is constructed from collisionless particles, all of the same rest mass. At every point on the shell the particles move isotropically in the plane perpendicular to the radius. Each particle moves in a bound orbit, determined by solving the scalar field and particle motion equations simultaneously. Initially we place the particles in circular orbits. Here we show a Quicktime movie of the shell for a moderately strong field configuration R=8M0. First we zoom into the surface of the shell to show that it is composed of orbiting particles.