Nonmodal Linear Stability of the Schwarzschild Black Hole

Abstract

A proof is given that the spaceLof solutions of the linearized vacuum Einstein equation around aSchwarzschild black hole is parametrized by two scalar fields, which are gauge invariant combinations ofperturbed algebraic and differential invariants of the Weyl tensor and encode the information on the odd (−)and even (þ) sectorsL . These fields measure the distortion of the geometry caused by a genericperturbation and are shown to be pointwise bounded on the outer regionr≥2M.