The Timelike Tube Theorem in Curved Spacetime

The timelike tube theorem asserts that in quantum field theory without gravity, the algebra of observables in an open set U is the same as the corresponding algebra of observables in its “timelike envelope” E(U), which is an open set that is in general larger. The theorem was originally proved in the 1960’s by Borchers and Araki for quantum fields in Minkowski space. Here we sketch the proof of a version of the theorem for quantum fields in a general real analytic spacetime. Details have appeared elsewhere.