Linearization Instability of Chiral Gravity

TL;DR

This paper demonstrates that topologically massive gravity exhibits a linearization instability at the chiral gravity limit, with certain perturbative modes failing to approximate true solutions, impacting classical and quantum analyses.

Contribution

It identifies a linearization instability in chiral gravity and shows that some linearized modes do not belong to the true phase space, revealing limitations of naive perturbation theory.

Findings

Linearization instability exists at the chiral gravity limit.

Degeneracy of the symplectic structure for perturbative modes.

Naive linearized solutions do not correspond to exact solutions.

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 $AdS_3$. 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.