Black hole stability under odd-parity perturbations in Horndeski gravity

Abstract

We study the stability under linear odd-parity perturbations of static spherically symmetric black holes in Horndeski gravity. We derive the master equation for these perturbations and obtain the conditions of no-ghost and Laplacian instability. In order for the black hole solutions to be stable, we study their generalized "Regge-Wheeler potential". It turns out that the problem is reduced to an algebraic problem where three functions characterizing the black hole should be positive outside the horizon to prove the stability. We found that these conditions are similar to the no-ghost and Laplacian instability conditions. We apply our results to various known solutions.

10 pages, 1 figure, slightly extended introduction, results unchanged

References in corpus (6)

• Covariant Galileon
• Avoiding Dark Energy with 1/R Modifications of Gravity
• Black holes with non-minimal derivative coupling
• DGP Specteroscopy
• Stability of Schwarzschild-like solutions in f(R,G) gravity models
• Master Equations for Gravitational Perturbations of Static Lovelock Black Holes in Higher Dimensions

Cited by in corpus (17)

• Horndeski theory and beyond: a review
• Hamiltonian vs stability and application to Horndeski theory
• The mass-radius relation for neutron stars in $f(R)=R+\alpha R^2$ gravity: a comparison between purely metric and torsion formulations
• Black hole perturbations in modified gravity
• Thin-Shell Wormhole Satisfying Energy Conditions
• Topological black hole in the theory with nonminimal derivative coupling with power-law Maxwell field and its thermodynamics
• Pure Lovelock black hole in the dimension, $d=3N+1$, is stable
• Dynamic instability analysis for bumblebee black holes: the odd parity
• Quasi-Normal Modes of Hairy Scalar Tensor Black Holes: Odd Parity
• Testing the Speed of Gravity with Black Hole Ringdown
• Quasi-normal Modes of Static Spherically Symmetric Black Holes in $f(R)$ Theory
• Black holes in new massive conformal gravity
• Stability of generalized Einstein-Maxwell-scalar black holes
• Gravitational odd-parity perturbation of a Horndeski hairy black hole: quasinormal mode and parameter constraint
• Axial perturbations of black holes in scalar-tensor gravity: near-horizon behaviour
• Static topological black hole with nonminimal derivative coupling and nonlinear electromagnetic field of Born-Infeld type
• Extremal cosmological black holes in Horndeski gravity and the anti-evaporation regime