Constraining the deformation of a black hole mimicker from the shadow

TL;DR

This paper investigates the shadow of a black hole mimicker described by the $\, ext{ extdelta}$-Kerr metric, analyzing its optical properties and constraining its deformation parameter based on observational data from M87's supermassive compact object.

Contribution

It provides a detailed ray-tracing analysis of the $\, extdelta$-Kerr metric's shadow and assesses observational constraints on its deformation parameter, comparing it with Kerr black holes.

Findings

The shadow shape of the $\, extdelta$-Kerr metric can resemble that of a Kerr black hole.

Current shadow observations cannot exclude the $\, extdelta$-Kerr solution.

Constraints on the deformation parameter are limited by observational uncertainties.

Abstract

We consider a black hole mimicker given by an exact solution of the stationary and axially symmetric field equations in vacuum known as the $\delta$-Kerr metric. We study its optical properties based on a ray-tracing code for photon motion and characterize the apparent shape of the shadow of the compact object and compare it with the Kerr black hole. For the purpose of obtaining qualitative estimates related to the observed shadow of the supermassive compact object in the galaxy M87 we focus on values of the object's spin $a$ and inclination angle of observation $\theta_0$ close to the measured values. We then apply the model to the shadow of the $\delta$-Kerr metric to obtain onstraints on the allowed values of the deformation parameter. We show that based uniquely on one set of observations of the shadow's boundary it is not possible to exclude the $\delta$-Kerr solution as a viable source for the geometry in the exterior of the compact object.