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Gravitational quasinormal radiation of higher-dimensional black holes

R. A. Konoplya

TL;DR

This work computes gravitational quasinormal modes for higher-dimensional black holes—Schwarzschild, Reissner–Nordström, and spacetimes with positive or negative cosmological constant—using the Ishibashi–Kodama scalar, vector, and tensor perturbation framework. By applying a 6th-order WKB method and the Horowitz–Hubeny approach for AdS cases, it reveals that the three perturbation types yield distinct QNM spectra in $D>4$, with scalar-type modes generally damped most slowly and thus dominating late-time ringing. The study also clarifies how a nonzero cosmological constant shifts the spectra (SdS and SAdS differently) and how charge couples electromagnetic and gravitational perturbations, showing breaking of isospectrality and the absence of purely EM or gravitational modes in higher dimensions. Overall, the results illuminate stability and gravitational radiation characteristics of higher-dimensional BHs and have implications for brane models and AdS/CFT contexts.

Abstract

We find the gravitational resonance (quasinormal) modes of the higher dimensional Schwarzschild and Reissner-Nordstrem black holes. The effect on the quasinormal behavior due to the presence of the $λ$ term is investigated. The QN spectrum is totally different for different signs of $λ$. In more than four dimensions there excited three types of gravitational modes: scalar, vector, and tensor. They produce three different quasinormal spectra, thus the isospectrality between scalar and vector perturbations, which takes place for D=4 Schwarzschild and Schwarzschild-de-Sitter black holes, is broken in higher dimensions. That is the scalar-type gravitational perturbations, connected with deformations of the black hole horizon, which damp most slowly and therefore dominate during late time of the black hole ringing.

Gravitational quasinormal radiation of higher-dimensional black holes

TL;DR

This work computes gravitational quasinormal modes for higher-dimensional black holes—Schwarzschild, Reissner–Nordström, and spacetimes with positive or negative cosmological constant—using the Ishibashi–Kodama scalar, vector, and tensor perturbation framework. By applying a 6th-order WKB method and the Horowitz–Hubeny approach for AdS cases, it reveals that the three perturbation types yield distinct QNM spectra in , with scalar-type modes generally damped most slowly and thus dominating late-time ringing. The study also clarifies how a nonzero cosmological constant shifts the spectra (SdS and SAdS differently) and how charge couples electromagnetic and gravitational perturbations, showing breaking of isospectrality and the absence of purely EM or gravitational modes in higher dimensions. Overall, the results illuminate stability and gravitational radiation characteristics of higher-dimensional BHs and have implications for brane models and AdS/CFT contexts.

Abstract

We find the gravitational resonance (quasinormal) modes of the higher dimensional Schwarzschild and Reissner-Nordstrem black holes. The effect on the quasinormal behavior due to the presence of the term is investigated. The QN spectrum is totally different for different signs of . In more than four dimensions there excited three types of gravitational modes: scalar, vector, and tensor. They produce three different quasinormal spectra, thus the isospectrality between scalar and vector perturbations, which takes place for D=4 Schwarzschild and Schwarzschild-de-Sitter black holes, is broken in higher dimensions. That is the scalar-type gravitational perturbations, connected with deformations of the black hole horizon, which damp most slowly and therefore dominate during late time of the black hole ringing.

Paper Structure

This paper contains 9 sections, 23 equations, 2 figures, 3 tables.

Table of Contents

  1. Introduction and basic equations
  2. Schwarzschild
  3. $\Lambda$-term
  4. Schwarzschild-de-Sitter
  5. Schwarzschild-anti-de-Sitter
  6. Charge
  7. Appendix. Quasinormal modes of $D=4$ RN BH
  8. Discussion
  9. Acknowledgments

Figures (2)

  • Figure 1: SdSBH: $\omega_{Re}$ as a function of $\Lambda$ for vector-type modes in the 6th order WKB approximation, $l=3$$n=0$; $D=5$ (bottom), $6$, $7$ (top).
  • Figure 2: SdSBH: $\omega_{Im}$ as a function of $\Lambda$ for vector-type modes in the 6th order WKB approximation, $l=3$$n=0$; $D=5$ (bottom), $6$, $7$ (top).