# Near-extremal black holes in Weyl gravity: Quasinormal modes and geodesic instability

## TL;DR

This paper investigates the stability and quasinormal modes of nearly extremal Weyl gravity black holes, deriving exact relations and exploring their implications for black hole physics and quantum gravity connections.

## Contribution

It provides an exact relation for quasinormal modes of scalar perturbations in nearly extreme Weyl gravity black holes and analyzes their stability and geodesic properties.

## Key findings

- Derived a lower bound on event horizon radius for stability.
- Found highly damped quasinormal modes linked to the Barbero-Immirzi parameter.
- Calculated Lyapunov exponent and angular velocity of unstable null geodesics.

## Abstract

Stability criteria of nearly extreme black holes in the perturbations level is one of the interesting issues in gravitational systems. Considering the nearly extreme conformal-de Sitter black holes, in this paper, we obtain an exact relation for the quasinormal modes of scalar perturbations. As for stability criteria, we find a lower bound on the event horizon radius which is corresponding to an upper bound on the value of the quasinormal frequencies. In addition, we show that the asymptotic behavior of quasinormal modes gives highly damped modes which is important due to possible connection between their real part and the Barbero-Immirzi parameter. We also obtain the Lyapunov exponent and the angular velocity of unstable circular null geodesics. Finally, we examine the validity of the relation between calculated quasinormal modes and unstable circular null geodesics.