# Black holes in new massive conformal gravity

## TL;DR

This paper studies black holes in a modified gravity theory, revealing the instability of small Schwarzschild black holes and the emergence of new black hole solutions with Ricci tensor and scalar hair.

## Contribution

It demonstrates the instability of Schwarzschild black holes in new massive conformal gravity and introduces a new class of black holes with Ricci tensor and scalar hair.

## Key findings

- Small Schwarzschild black holes are unstable.
- New black holes with Ricci tensor and scalar hair appear.
- Instability leads to non-BBMB black hole solutions.

## Abstract

We investigate the black holes in the new massive conformal gravity which is not invariant under conformal transformations because of the presence of the Einstein-Hilbert term. First, we show that the small Schwarzschild black hole is unstable against the $s$-mode of linearized Ricci tensor by solving the Lichnerowicz-Ricci tensor equation. This instability induces the appearance of the non-BBMB (Bocharova-Bronnikov-Melnikov-Bekenstein) black hole that has both Ricci tensor and conformal scalar hair.