New massive conformal gravity

TL;DR

This paper explores a new form of massive conformal gravity, analyzing its gravitational wave modes, stability conditions, and black hole perturbation behavior, highlighting differences from traditional conformal gravity.

Contribution

It introduces and examines a new massive conformal gravity model, detailing its polarization modes, stability criteria, and black hole perturbation properties.

Findings

Identifies five polarization modes of gravitational waves in the model.

Shows Minkowski spacetime stability depends on non-negative mass squared.

Finds small Schwarzschild black holes are unstable against certain perturbations.

Abstract

We investigate the new massive conformal gravity which is not invariant under conformal transformations, in comparison to the massive conformal gravity. We find five polarization modes of gravitational waves propagating on the Minkowski spacetimes. The stability of Minkowski spacetimes is guaranteed if the mass squared is not negative and the linearized Ricci tenor is employed to describe a massive spin-2 graviton. However, the small Schwarzschild black hole is unstable against the $s$-mode massive graviton perturbations.