Time Evolution of Black Hole Perturbations in Quadratic Gravity

TL;DR

This paper investigates the time evolution of gravitational perturbations in black holes within Einstein-Weyl gravity, revealing universal late-time tails and limitations of traditional quasinormal mode analysis.

Contribution

It provides the first detailed time-domain analysis of black hole perturbations in quadratic gravity, highlighting universal decay tails and the breakdown of eikonal correspondence.

Findings

Late-time tails decay as t^{-5/6}

Eikonal correspondence breaks down in this context

Black hole stability range confirmed

Abstract

We study the full time-domain evolution of gravitational perturbations in black hole spacetimes arising in Einstein-Weyl gravity, a renormalizable extension of general relativity containing quadratic curvature corrections. We analyze both Schwarzschild and non-Schwarzschild solutions, focusing on monopole and higher multipole perturbations. Using semi-analytical methods based on the Rezzolla-Zhidenko parametrization for approximation of the black hole spacetime and time-domain integration for analysis of evolution of perturbations, we study the late-time behavior of gravitational perturbations. Our results show that the ringdown phase is followed by universal slowly decaying oscillatory tails with the envelope $ \psi \propto t^{-5/6} $. We also demonstrate the breakdown of the eikonal correspondence between quasinormal modes and unstable null geodesics, highlighting limitations of the WKB method in this context. Our analysis confirms the range of (in)stability of black holes in Einstein-Weyl gravity found in recent publications.