# Connection Between the Shadow Radius and Quasinormal Modes in Rotating
Spacetimes

Research paper by **Kimet Jusufi**

Indexed on: **10 Apr '20**Published on: **08 Apr '20**Published in: **arXiv - General Relativity and Quantum Cosmology**

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#### Abstract

Based on the geometric-optics correspondence between the parameters of a
quasinormal mode and the conserved quantities along geodesics, we propose an
equation to calculate the typical shadow radius for asymptotically flat and
rotating black holes when viewed from the equatorial plane given by
\begin{equation}\notag \bar{R}_s=\frac{\sqrt{2}}{2}\left(\sqrt{\frac{
r_0^{+}}{f'(r)|_{r_0^{+}}}}+\sqrt{\frac{ r_0^{-}}{f'(r)|_{r_0^{-}}}}\right),
\end{equation} with $r_0^{\pm}$ being the radius of circular null geodesics for
the corresponding mode. Furthermore we have explicitly related the shadow
radius to the real part of QNMs in the eikonal regime corresponding to the
prograde and retrograde mode, respectively. As a particular example, we have
computed the typical black hole shadow radius for some well known black hole
solutions including the Kerr black hole, Kerr-Newman black hole and higher
dimensional black hole solutions described by the Myers-Perry black hole.