Topologically massive gravity as a Pais-Uhlenbeck oscillator

TL;DR

This paper analyzes topologically massive gravity in 2+1 dimensions, showing it can be described as a ghost-free Pais-Uhlenbeck oscillator in certain parameter regimes, with detailed spectral and Newtonian limit analysis.

Contribution

It demonstrates that linearized topologically massive gravity reduces to a degenerate Pais-Uhlenbeck oscillator, providing new insights into its ghost-free higher derivative structure.

Findings

Linearized theory is Jordan-diagonalizable at specific parameter ratios.

The theory reduces to a degenerate Pais-Uhlenbeck oscillator.

The model is ghost-free despite higher derivatives.

Abstract

We give a detailed account of the free field spectrum and the Newtonian limit of the linearized "massive" (Pauli-Fierz), "topologically massive" (Einstein-Hilbert-Chern-Simons) gravity in 2+1 dimensions about a Minkowski spacetime. For a certain ratio of the parameters, the linearized free theory is Jordan-diagonalizable and reduces to a degenerate "Pais-Uhlenbeck" oscillator which, despite being a higher derivative theory, is ghost-free.