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  • Letter

Exact analytic photon escape cones and silhouettes for extremal Kerr black holes

Joshua Baines* and Matt Visser†

  • *Contact author: joshua.baines@sms.vuw.ac.nz
  • †Contact author: matt.visser@sms.vuw.ac.nz

Phys. Rev. D 111, L021501 – Published 6 January, 2025

DOI: https://doi.org/10.1103/PhysRevD.111.L021501

Abstract

Herein we exhibit exact, analytic, fully explicit, photon escape cones and the related silhouettes (“shadows”) at arbitrary distance from an extremal (|a|=m) Kerr black hole. In contrast to the situation for nonextremal (0<|a|<m) Kerr, where one typically has to resort to numerical, and/or graphics based, and/or perturbative investigations, the situation for extremal Kerr is amenable to direct analytic and fully explicit investigation. Interest in these results is twofold: In view of the technical complexity of Kerr spacetime, any fully explicit analytic result (even if only for the special case of extremality) is a significant aid to physical insight. Furthermore a significant fraction of observationally accessible galactic black holes are high spin, relatively close to extremal, objects (|a|≳0.85m) so the extremal case is a good analytically tractable zeroth order approximation for such objects.

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