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We study the linearization of the Dirichlet-to-Neumann map forPoincar\'e-Einstein metrics in even dimensions on an arbitrary compact manifoldwith boundary. By fixing a suitable gauge, we make the linearized Einsteinequation elliptic. In this gauge the linearization of the Dirichlet-to-Neumannmap appears as the scattering matrix for an elliptic operator of 0-type,modified by some differential operators. We study the scattering matrix byusing the 0-calculus and generalize a result of Graham for the case of thestandard hyperbolic metric on a ball.

Dirichlet-to-Neumann Map for Poincar\'e-Einstein Metrics in Even Dimensions