Constraint damping on subextremal Kerr spacetimes

Abstract

In the context of hyperbolic formulations of Einstein's field equations obtained via gauge fixing, constraint damping is a desirable feature that ensures that violations of the gauge condition and thus of the constraint equations are suppressed in evolution. Besides its utility in numerical relativity, it has played a key role in several (linear and nonlinear) stability proofs of spacetimes as solutions of the Einstein equations. In this paper, we show that an enhanced form of constraint damping can be implemented for the linearization of the Einstein equations around any subextremal Kerr black hole metric. The results proved here are a key ingredient in the author's proof of the nonlinear stability of the subextremal Kerr family.