Highly damped quasinormal modes of Kerr black holes

By Emanuele Berti, V. Cardoso, Shijun Yoshida. 2003

143 citations recorded by the source corpus.

Motivated by recent suggestions that highly damped black hole quasinormal modes (QNM's) may provide a link between classical general relativity and quantum gravity, we present an extensive computation of highly damped QNM's of Kerr black holes. We perform the computation using two independent numerical codes based on Leaver's continued fraction method. We do not limit our attention to gravitational modes, thus filling some gaps in the existing literature. As already observed by Berti and Kokkotas, the frequency of gravitational modes with $l=m=2$ tends to ${\ensuremath{\omega}}_{R}=2\ensuremath{\Omega},$ $\ensuremath{\Omega}$ being the angular velocity of the black hole horizon. We show that, if Hod's conjecture is valid, this asymptotic behavior is related to reversible black hole transformations. Other highly damped modes with $mg0$ that we computed do not show a similar behavior. The real part of modes with $l=2$ and $ml0$ seems to asymptotically approach a constant value ${\ensuremath{\omega}}_{R}\ensuremath{\simeq}\ensuremath{-}m\ensuremath{\varpi},$ $\ensuremath{\varpi}\ensuremath{\simeq}0.12$ being (almost) independent of a. For any perturbing field, trajectories in the complex plane of QNM's with $m=0$ show a spiraling behavior, similar to the one observed for Reissner-Nordstr\"om black holes. Finally, for any perturbing field, the asymptotic separation in the imaginary part of consecutive modes with $mg0$ is given by $2\ensuremath{\pi}{T}_{H}$ ${(T}_{H}$ being the black hole temperature). We conjecture that for all values of l and $mg0$ there is an infinity of modes tending to the critical frequency for superradiance $({\ensuremath{\omega}}_{R}=m)$ in the extremal limit. Finally, we study in some detail modes branching off the so-called ``algebraically special frequency'' of Schwarzschild black holes. For the first time we find numerically that QNM multiplets emerge from the algebraically special Schwarzschild modes, confirming a recent speculation.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/2d860d88964a2774d1f2a94f6623402e4df684bf

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

In Nuclear and High Energy Physics

Citations in the corpus

Gravity and the thermodynamics of horizons (2005, background): “y there has been some rethinking on this issue due to the following consideration: For a classical black hole, one can deﬁne a class of solutions to wave equations called quasi normal modes [see e.g.,[132,133,134,135]]. These modes have discrete frequencies which are complex, given by ωn = i n+(1/2)”
Gravity and the Thermodynamics of Horizons (2003, background): “…recently there has been some rethinking on this issue due to the following consideration: For a classical black hole, one can define a class of solutions to wave equations called quasi normal modes [see e.g.,Berti et al. (2003); Cardoso et al. (2003); Corichi (2003); Kokkotas and Schmidt (1999)].”