Near-horizon gravitational perturbations of rotating black holes

Abstract

Perturbative calculations of gravitational radiation near the horizons of rotating black holes in the frequency domain have been plagued by divergence issues. We resolve this longstanding obstacle by constructing a nonsingular source term for near-horizon gravitational perturbations, or equivalently perturbed Weyl scalars $ψ_0$ with a spin weight of $s = +2$, within the generalized Sasaki-Nakamura formalism for the first time. As illustrative applications, we compute the dynamical deformation of the event horizon induced by an ultrarelativistic particle plunge, demonstrating the excitation of quasinormal modes at the horizon, and we evaluate the energy flux towards the horizon from an extreme mass-ratio inspiral. This work provides a powerful tool for studying physics near black hole horizons.

Figures (3)

• Figure 1: The induced waveform of the perturbed shear for the $\ell = 2$ mode at the horizon $\sigma(r \to r_{+})$ by an ultrarelativistic particle falling radially into a nonrotating , viewing at $\Theta=\pi/2$, $\Phi=0$. The and Teukolsky+regularization (T+R) approaches agree very well.
• Figure 2: The best fit using gravitational (dashed) on the shear waveform in Figure \ref{['fig:Waveform_hor']} (solid). The fit uses $\ell = 2$ and $n = 0 \dots 7$ overtones, achieving a mismatch of $3.32\times 10^{-9}$.
• Figure 3: The absolute value of energy flux towards the horizon for $a=0.9M$, $p=6M$, $e=0.7$, $x=\cos\pi/4$. The mode indexes are $\ell=m=2$ and $\ell=m=4$ with polar index $k=0$ and radial index $n=0$ to $n=80$. The two dashed lines mark the transition of the energy flux from being negative to positive due to the sign change of $\kappa$. For $\ell=2$, this transition occurs between $n=30$ and $n=31$; for $\ell=4$, it takes place between $n=61$ and $n=62$. The - and Teukolsky (using pybhpt) approaches agree very well.