Is a black hole shadow a reliable test of the no-hair theorem?

TL;DR

This paper investigates whether black hole shadow imaging can reliably test the no-hair theorem, finding that non-Kerr multipolar structures can produce similar shadows, thus complicating such tests.

Contribution

It demonstrates that higher multipole moments introduce degeneracy in shadow shapes, challenging the use of shadows to confirm the Kerr nature of black holes.

Findings

Higher multipole moments cause shadow degeneracy.

Non-Kerr objects can mimic Kerr-like shadows.

Shadow shape alone may not confirm the no-hair theorem.

Abstract

Capturing the image of the shadow cast by the event horizon of an illuminated black hole is, at the most basic level, an experiment of extreme light deflection in a strongly curved spacetime. As such, the properties of an imaged shadow can be used to probe the general relativistic Kerr nature of astrophysical black holes. As an example of this prospect, it is commonly asserted that a shadow can test the validity of the theory's famous `no hair theorem' for the black hole's mass and spin multipole moments. In this paper, we assess this statement by calculating the shadow's equatorial radius in spacetimes with an arbitrary multipolar structure and within a slow rotation approximation. We find that when moments higher than the quadrupole are taken into account, the shadow acquires a high degree of degeneracy as a function of the deviation from the Kerr multipole moments. The results of our analysis suggest that dark objects with strongly non-Kerr multipolar structure could nevertheless produce a Kerr-like shadow with its characteristic quasi-circular shape.