Degrees of freedom of weak gravitational field on a spherically symmetric background

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Written by Piotr Waluk

We present a way of reducing ADM data for the Cauchy problem for linearized gravity on a Kottler background (i.e. general spherically symmetric vacuum solution with cosmological constant)  to a set of four gauge-invariant unconstrained scalar functions on the initial surface, containing whole information about the perturbation. This is a generalization of earlier results by J. Jezierski and J. Kijowski for Minkowski and Schwarzschild backgrounds.