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

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.

9 pages with one captioned figure and a table. Accepted in PRD

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• Quasinormal modes of self-dual black holes in loop quantum gravity
• Conformal Weyl gravity via two stages of quasinormal ringing and late-time behavior
• Quasinormal modes of black holes in Weyl gravity: Electromagnetic and gravitational perturbations
• Stability and phase transition of rotating Kaluza-Klein black holes
• Quasi-normal Modes of near-extremal black holes in Generalized spherically symmetric spacetime and Strong Cosmic Censorship Conjecture
• Self-dual Gravitational Instantons in Conformal Gravity: Conserved Charges and Thermodynamics
• Quasinormal Modes in Near-Extremal Spinning C-Metric
• Nöther Currents, Black Hole Entropy Universality and CFT Duality in Conformal Weyl Gravity
• Quasinormal Modes of Near-Extremal Black Holes and Black Strings in Massive Gravity Background