Ringdown waves from hairy black holes

Abstract

We derive general formulas for quasi-normal mode (QNM) frequencies of hairy black holes by exploiting the QNM--geodesic correspondence. The black hole hair is treated as an anisotropic fluid perturbatively added to the vacuum black holes (Schwarzschild and Kerr black holes). Under this setting, independent of energy conditions, our formulas offer a systematic method to compute quasi-normal mode frequencies for a broad class of hairy black holes.

Figures (8)

• Figure 1: Tangential pressure parameter $w_\theta(r)$ and QNM shifts for the Bardeen black hole.
• Figure 2: Tangential pressure parameter $w_\theta(r)$ and frequency shifts for the Hayward black hole.
• Figure 3: QNM shifts for different values of $w_q$. Continuous lines refer to $\delta\Omega / \Omega_0$ and dashed lines refer to $\delta\lambda / \lambda_0$ for different values of $k$.
• Figure 4: Representative QNM and geometric shifts for the anisotropic fluid halo Kiselev model.
• Figure 5: Time evolution of the ringdown waveform, $\Psi(t)=\Re\!\left[e^{-i\,\omega_{\rm QNM} t}\right]$. We compare the amplitudes within the different models for the quasinormal mode $n=0$ and $\ell=4$ (Eikonal limit). Although $\ell=4$ may not appear to be a large enough value to justify the eikonal approximation, even the $\ell=4$ case provides very accurate predictions, as has already been pointed out by the existing literature Iyer:1986nqBerti:2005eb.