Measurement of the Kerr Spin Parameter by Observation of a Compact Object's Shadow

TL;DR

This paper proposes a method to determine the spin and inclination of a Kerr black hole by analyzing the shape of its shadow, extending the technique to naked singularities.

Contribution

It introduces a new observational technique to measure black hole spin and inclination from shadow shape, including cases of naked singularities.

Findings

Spin and inclination can be estimated from shadow shape observables.

Method applicable to Kerr black holes and naked singularities.

Potential for observational determination of black hole parameters.

Abstract

A black hole casts a shadow as an optical appearance because of its strong gravitational field. We study how to determine the spin parameter and the inclination angle by observing the apparent shape of the shadow, which is distorted mainly by those two parameters. Defining some observables characterizing the apparent shape (its radius and distortion parameter), we find that the spin parameter and inclination angle of a Kerr black hole can be determined by the observation. This technique is also extended to the case of a Kerr naked singularity.