  We present a new general method for proving global decay of energy through a
suitable spacetime foliation, as well as pointwise decay, starting from an
integrated local energy decay estimate. The method is quite robust, requiring
only physical space techniques, and circumvents use of multipliers or
commutators with weights growing in t. In particular, the method applies to a
wide class of perturbations of Minkowski space as well as to Schwarzschild and
Kerr black hole exteriors.
