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We prove a uniform weighted resolvent estimate for the massless Klein-Gordonoperator on a curved spacetime which is sufficiently close to the Minkowskispacetime. This particularly implies the existence and H\"{o}lder continuity ofthe limiting resolvents at all energies, as well as the absolute continuity, ofthe massless Klein-Gordon operator. The proof is based on a simple version ofMourre's commutator method and does not rely on microlocal analysis. We alsoprove the absence of eigenvalues via the Virial theorem under an ellipticitycondition on the commutator of the massless Klein-Gordon operator against thegenerator of a wick-rotated dilation, which is weaker than the smallnesscondition for the metric perturbation.

Limiting absorption principle and absence of eigenvalues for massless Klein-Gordon operators on perturbations of the Minkowski spacetime