Bachian Gravity in Three Dimensions

TL;DR

This paper explores modifications of three-dimensional gravity theories based on the Bach tensor, analyzing their spectra, conserved quantities, and black hole solutions, expanding understanding of massive gravitons in lower-dimensional spacetimes.

Contribution

It introduces a generic construction of three-dimensional Bachian gravity models and analyzes their physical properties, including spectra and conserved charges, without relying solely on a metric-based Lagrangian.

Findings

Constructed a generic class of Bachian gravity models in 3D.

Analyzed the spectra of these models and identified massive graviton modes.

Computed conserved quantities for BTZ black holes within these theories.

Abstract

In three dimensions, there exist modifications of Einstein's gravity akin to the topologically massive gravity that describe massive gravitons about maximally symmetric backgrounds. These theories are built on the three-dimensional version of the Bach tensor (a curl of the Cotton-York tensor) and its higher derivative generalizations; and they are on-shell consistent without a Lagrangian description based on the metric tensor alone. We give a generic construction of these models, find the spectra and compute the conserved quantities for the Banados-Teitelboim-Zanelli black hole.