Linearization Instability of Chiral Gravity

Abstract

Carrying out an analysis of the constraints and their linearizations on a spacelike hypersurface, we show that topologically massive gravity has a linearization instability at the chiral gravity limit about $Ad{S}_3$. We also calculate the symplectic structure for all the known perturbative modes (including the log-mode) for the linearized field equations and find it to be degenerate (non-invertible) hence these modes do not approximate exact solutions and so do not belong to the linearized phase space of the theory. Naive perturbation theory fails: the linearized field equations are necessary but not sufficient in finding viable linearized solutions. This has important consequences for both classical and possible quantum versions of the theory.

arXiv comment6 pages, version to appear in PRD

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• Lee-Wald Charge and Asymptotic Behaviors of the Weyl-invariant Topologically Massive Gravity
• Linearization Instability in Gravity Theories
• Consistency conditions for O-plane unsmearing from second-order perturbation theory
• Linearization (in)stabilities and crossed products
• Second Order Gauge Invariant Perturbation Theory and Conserved Charges in Cosmological Einstein's Gravity