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 equation. In this paper, we show that an enhanced form of constraint damping can be implemented for the linearization of the Einstein equation around any subextremal Kerr black hole metric: the constraint propagation wave operator satisfies mode stability and has an arbitrarily large indicial gap at zero energy. The results proved here are a key ingredient in the author's proof of the nonlinear stability of the subextremal Kerr family.
Related
- Mode stability for the Klein-Gordon equation on subextremal Kerr-de Sitter spacetimes
- Price's law for scalar waves on 1+4 dimensional subextremal Myers-Perry spacetimes
- Kerr stability in the full subextremal range
- Generalized Whiting transform and Flux Estimates for Wave Equations in Subextremal Kerr
- Quasinormal modes on Kerr spacetimes
BibTeX
@misc{hintz2026constraint,
title = {{Constraint damping on subextremal Kerr spacetimes}},
author = {Peter Hintz},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.27658},
eprint = {2606.27658},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.27658},
}
RIS
TY - UNPB
TI - Constraint damping on subextremal Kerr spacetimes
AU - Peter Hintz
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2606.27658
UR - https://arxiv.org/abs/2606.27658
AB - 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 equation. In this paper, we show that an enhanced form of constraint damping can be implemented for the linearization of the Einstein equation around any subextremal Kerr black hole metric: the constraint propagation wave operator satisfies mode stability and has an arbitrarily large indicial gap at zero energy. The results proved here are a key ingredient in the author's proof of the nonlinear stability of the subextremal Kerr family.
ER -