Black holes in multimetric gravity. II. Hairy solutions and linear stability of the non- and partially proportional branches

Wood, Kieran; Saffin, Paul M.; Avgoustidis, Anastasios

Abstract

Owing to our work in part I of this series of papers, it is understood that the analytically known black hole solutions in the theory of ghost-free multimetric gravity can be split into three distinct classes and that one of these classes—the proportional branch—exhibits the Gregory-Laflamme instability at linear level in the metric perturbations, whenever the black hole horizon size is smaller than (roughly) the Compton wavelength of the theory’s lightest massive graviton. In this first of two sequels, we determine the linear stability of the two remaining classes of black hole solutions—the nonproportional and partially proportional branches—and discuss how our results likely differ at nonlinear level. We also give a general prescription to construct multimetric solutions describing black holes endowed with massive graviton hair, which may constitute the end state of the instability in the proportional branch. We utilize a tractable example model involving three metrics to see how this works in practice and determine the asymptotic form of its corresponding hairy solutions at infinity, where one can clearly see the individual contributions from each of the graviton mass modes.

Citation

Wood, K., Saffin, P. M., & Avgoustidis, A. (2025). Black holes in multimetric gravity. II. Hairy solutions and linear stability of the non- and partially proportional branches. Physical Review D, 111(2), Article 024057. https://doi.org/10.1103/PhysRevD.111.024057

• Journal Article Type: Article
• Acceptance Date: Jan 5, 2025
• Online Publication Date: Jan 23, 2025
• Publication Date: Feb 1, 2025
• Deposit Date: Jan 28, 2025
• Publicly Available Date: Jan 28, 2025
• Journal: Physical Review D
• Print ISSN: 2470-0010
• Electronic ISSN: 2470-0029
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 111
• Issue: 2
• Article Number: 024057
• DOI: https://doi.org/10.1103/PhysRevD.111.024057
• Keywords: Alternative gravity theories; Classical black holes; Gravity in dimensions other than four; Gravitons
• Public URL: https://nottingham-repository.worktribe.com/output/44538466
• Publisher URL: https://journals.aps.org/prd/abstract/10.1103/PhysRevD.111.024057