Can different black holes cast the same shadow?
Haroldo C. D. Lima Junior, Lu\'is C. B. Crispino, Pedro V. P. Cunha, and Carlos A. R. Herdeiro

TL;DR
This paper investigates conditions under which different black hole spacetimes can produce identical shadows, revealing that shadow degeneracy does not necessarily imply identical horizon geometries or lensing effects.
Contribution
It classifies shadow-degenerate black hole geometries in spherical and stationary, axisymmetric cases, providing explicit examples and conditions for shadow degeneracy.
Findings
Two classes of shadow-degenerate geometries in spherical symmetry.
Explicit examples of metrics with identical shadows but different horizons.
Shadow degeneracy does not guarantee identical lensing effects.
Abstract
We consider the following question: may two different black holes (BHs) cast exactly the same shadow? In spherical symmetry, we show the necessary and sufficient condition for a static BH to be shadow-degenerate with Schwarzschild is that the dominant photonsphere of both has the same impact parameter, when corrected for the (potentially) different redshift of comparable observers in the different spacetimes. Such shadow-degenerate geometries are classified into two classes. The first shadow-equivalent class contains metrics whose constant (areal) radius hypersurfaces are isometric to those of the Schwarzschild geometry, which is illustrated by the Simpson and Visser (SV) metric. The second shadow-degenerate class contains spacetimes with different redshift profiles and an explicit family of metrics within this class is presented. In the stationary, axi-symmetric case, we determine a…
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