Gravitational waves in general relativity II. The reflexion of cylindrical waves

Abstract

The reflexion of outward travelling cylindrical gravitational waves by a thin cylindrical shell of matter is discussed. The shell is regarded as a surface distribution, and it is shown that if it is perfectly rigid, total reflexion occurs. Quasi-periodic incident waves are found to lead to a completely periodic standing wave state between the reflector and a central wave-source, the field outside the system remaining static. In the treatment of standing waves the components of the stress-energy tensor in the shell are determined and the construction for a model source is given.