Connection between the shadow radius and quasinormal modes in rotating spacetimes

2020/04/30 by Kimet Jusufi
Mathematics · Physics and Astronomy · #Angular momentum #Astrophysical Phenomena and Observations #Astrophysics and Cosmic Phenomena #Black hole (networking) #Connection (principal bundle) #Eikonal equation #Geodesic #Geometry #Mathematical physics #Mathematics #Physics #Plane (geometry) #Pulsars and Gravitational Waves Research #Quantum mechanics #Quasinormal mode #RADIUS #Rotating black hole #Shadow (psychology) #gr-qc

paper · pdf · doi:10.1103/physrevd.101.124063

published as Phys. Rev. D 101, 124063 (2020) · 8 pages, 4 figures. Published in Phys. Rev. D

arxiv created 2020/06/29 · openalex publication_date 2020/06/29 · arxiv updated 2020/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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 R_s=√(2)/2(√r₀⁺/f^\ensuremath'(r)|_r₀⁺+√r₀^\ensuremath-/f^\ensuremath'(r)|_r₀^\ensuremath-), with r₀^\ifmmode±\else\textpm\fi 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.

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