The Doppler effect in the field of a thick spherical shell

Abstract

The relativistic field of a thick spherical shell of matter is worthy of notice inasmuch as it provides the only known example of a Euclidean pocket in a Riemannian space-time. The boundary conditions are used to obtain correct expressions for the metric in different parts of the field and an inaccuracy of Combridge's treatment is removed. The constant of the Doppler effect which is a violet-shift, follows from the boundary conditions in an unforced manner.