# On the local structure of the Klein-Gordon field on curved spacetimes

August 31, 2000

This paper investigates wave-equations on spacetimes with a metric which is
locally analytic in the time. We use recent results in the theory of the
non-characteristic Cauchy problem to show that a solution to a wave-equation
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.

open access link

Lett.Math.Phys. 54 (2000) 249-261

Keywords:

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