# Characterizing black hole metrics in quadratic gravity

## TL;DR

This paper explores the properties of black hole solutions in quadratic gravity, analyzing how modifications to Einstein's theory affect black hole structure, thermodynamics, and stability, including effects of ghost modes and oscillatory solutions.

## Contribution

It provides a detailed characterization of black hole metrics in quadratic gravity, linking weak field behavior with strong gravity features and exploring ghost-related phenomena.

## Key findings

- Yukawa term influences black hole thermodynamics and singularity structure.
- Imaginary ghost mass leads to oscillatory solutions with specific wavelengths.
- Weak field limit includes massless graviton and spin-2 ghost effects.

## Abstract

The recent discovery of non-Schwarzschild black hole spacetimes has opened new directions of research in higher-derivative gravitational theories. However, despite intense analytical and numerical efforts, the link with the linearized theory is still poorly understood. In this work we address this point for the Einstein-Weyl Lagrangian, whose weak field limit is characterized by the standard massless graviton and a spin-2 ghost. We show that the strength of the Yukawa term at infinity determines the thermal properties of the black hole and the structure of the singularity near $r=0$. Moreover, inspired by recent results in the Asymptotic Safety scenario we investigate the consequences of an imaginary ghost mass. In this case we find a countable set of solutions all characterized by spatial oscillations of typical wavelength determined by the mass of the spin-2 field.