Correction to: Linear stability of slowly rotating Kerr black holes

Lemma 11.7 in 1 [1] is not correct as stated; we are very grateful to Lili He for pointing this out to us.Nonetheless, Theorem 1.1 remains true as stated.We recall the statement of Theorem 1.1:satisfy the linearized constraint equations, and decay according totogether with their derivatives along r∂ r and ∂ ω (spherical derivatives) up to order 8. Let h denote a solution of the linearized Einstein vacuum equation D g b Ric(h) = 0 on M • which attains the initial data γ , k at • 0 .Then there exist linearized black hole parameters ḃ = ( ṁ, ȧ) ∈ R × R 3 and a vector field V on M • such that1 All equation numbers etc. refer to [1] from now on, unless stated otherwise.