Quasi-Normal Modes in Topologically Massive Gravity

TL;DR

This work analyzes quasi-normal modes of tensor perturbations in topologically massive gravity on BTZ AdS3 and reveals that, for generic Chern-Simons coupling $m$, the QNM spectrum forms a descendent tower emanating from a seed mode that satisfies the first-order chiral equation $\epsilon_\mu^{\alpha\beta}\nabla_\alpha h_{\beta\nu}+m h_{\mu\nu}=0$. The authors exploit the local $SL(2,R)\times SL(2,R)$ structure of the BTZ background to construct QNMs via chiral highest-weight seeds, obtaining explicit left- and right-moving towers with frequencies $\omega^L_n=-k-2i(h_L(m)+n)$ and $\omega^R_n=k-2i(h_R(m)+n)$ (with $h_{L,R}(m)$ determined by the mass). At the special chiral points $m=\pm1$, gravitational QNMs are absent, consistent with a holographic dual that is a chiral CFT; the results illuminate how CS-induced chirality shapes real-time boundary correlators and raise questions about the role of non-geometric sectors in restoring dynamical features like Poincaré recurrence. Overall, the paper provides a concrete algebraic organization of QNMs in TM gravity and connects bulk decay channels to boundary CFT data via the $SL(2,R)\times SL(2,R)$ structure.

Abstract

We determine the black hole quasi-normal mode spectrum for tensor perturbations in topologically massive AdS-gravity. In the special case of chiral gravity quasi-normal modes are absent despite of the presence of a horizon. In the process we uncover a simple algebraic structure in the quasi normal modes spectrum: the tower of QNM's consists of descendents of a "chiral highest weight'' QNM which in turn satisfies a first order equation.