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We present a new general method for proving global decay of energy through asuitable spacetime foliation, as well as pointwise decay, starting from anintegrated local energy decay estimate. The method is quite robust, requiringonly physical space techniques, and circumvents use of multipliers orcommutators with weights growing in t. In particular, the method applies to awide class of perturbations of Minkowski space as well as to Schwarzschild andKerr black hole exteriors.

A new physical-space approach to decay for the wave equation with applications to black hole spacetimes