Black holes in massive conformal gravity

Yun Soo Myung

doi:10.1016/j.physletb.2014.01.044

Abstract

We analyze the classical stability of Schwarzschild black hole in massive conformal gravity which was recently proposed for another massive gravity model. This model in the Jordan frame is conformally equivalent to the Einstein–Weyl gravity in the Einstein frame. The coupled linearized Einstein equation is decomposed into the traceless and trace equation when one chooses 6m2φ=δR. Solving the traceless equation exhibits unstable modes featuring the Gregory–Laflamme s-mode instability of five-dimensional black string, while we find no unstable modes when solving the trace equation. It is shown that the instability of the black hole in massive conformal gravity arises from the massiveness where the geometry of extra dimension trades for mass.

Highlights

Massive conformal gravity was proposed as another massive gravity model [1]
This model is composed of a conformally coupled scalar to Einstein-Hilbert term and Weyl-squared term which are invariant under conformal transformations
If one takes into account the number of degrees of freedom (DOF), it is easy to show why the Schwarzschild black hole is physically stable in the Einstein gravity, whereas the Schwarzschild black hole is unstable in massive conformal gravity

Summary

Introduction

Massive conformal gravity was proposed as another massive gravity model [1] This model is composed of a conformally coupled scalar to Einstein-Hilbert term (conformal relativity) and Weyl-squared term which are invariant under conformal transformations. Massive conformal gravity plays a role of being massive gravity model [5, 6] because it includes Einstein-Hilbert term and Weyl-squared term in addition to a conformally coupled scalar. Solving the traceless equation exhibits unstable modes featuring the GL s-mode instability of five-dimensional black string, while we find no unstable modes from solving the trace equation This implies that massive conformal gravity could not provide the Schwarzschild black hole solution

Massive conformal gravity

Massive conformal gravity in Einstein frame

Instability of Schwarzschild black hole in massive conformal gravity

Discussions