# Lichnerowicz Modes and Black Hole Families in Ricci Quadratic Gravity

## TL;DR

This paper explores new black hole solutions in Ricci quadratic gravity, revealing a branch crossing point characterized by a Lichnerowicz eigenfunction, and discusses potential stability changes between branches based on thermodynamic and dynamical analyses.

## Contribution

It identifies a new branch of black hole solutions in Ricci quadratic gravity and links the crossing point to a Lichnerowicz eigenfunction, suggesting stability transitions.

## Key findings

- Existence of a new black hole branch crossing the Schwarzschild branch.
- The crossing point is associated with a static negative-eigenvalue eigenfunction.
- Potential stability switch between black hole branches for small radii.

## Abstract

A new branch of black hole solutions occurs along with the standard Schwarzschild branch in $n$-dimensional extensions of general relativity including terms quadratic in the Ricci tensor. The standard and new branches cross at a point determined by a static negative-eigenvalue eigenfunction of the Lichnerowicz operator, analogous to the Gross-Perry-Yaffe eigenfunction for the Schwarzschild solution in standard $n=4$ dimensional general relativity. This static eigenfunction has two r\^oles: both as a perturbation away from Schwarzschild along the new black-hole branch and also as a threshold unstable mode lying at the edge of a domain of Gregory-Laflamme-type instability of the Schwarzschild solution for small-radius black holes. A thermodynamic analogy with the Gubser and Mitra conjecture on the relation between quantum thermodynamic and classical dynamical instabilities leads to a suggestion that there may be a switch of stability properties between the old and new black-hole branches for small black holes with radii below the branch crossing point.