On the local structure of the KleinGordon field on curved spacetimes
Abstract
This paper investigates waveequations on spacetimes with a metric which is locally analytic in the time. We use recent results in the theory of the noncharacteristic Cauchy problem to show that a solution to a waveequation vanishing in an open set vanishes in the ``envelope'' of this set, which may be considerably larger and in the case of timelike tubes may even coincide with the spacetime itself. We apply this result to the real scalar field on a globally hyperbolic spacetime and show that the field algebra of an open set and its envelope coincide. As an example there holds an analog of Borchers' timelike tube theorem for such scalar fields and hence, algebras associated with world lines can be explicitly given. Our result applies to cosmologically relevant spacetimes.
 Publication:

arXiv eprints
 Pub Date:
 August 2000
 DOI:
 10.48550/arXiv.mathph/0008043
 arXiv:
 arXiv:mathph/0008043
 Bibcode:
 2000math.ph...8043S
 Keywords:

 Mathematical Physics;
 81T05;
 81T20;
 35L05;
 35L10;
 34A12
 EPrint:
 17 pages, LaTeX, minor corrections, figures added