Shadows of CPR black holes and tests of the Kerr metric

TL;DR

This paper analyzes the shadows of CPR black holes to understand how deviations from the Kerr metric affect observable features, highlighting the challenges and potential for testing general relativity with high-quality data.

Contribution

It investigates the impact of deformation parameters on black hole shadows, showing how they can mimic Kerr shadows and identifying features that could distinguish non-Kerr black holes.

Findings

Deformation parameter ε₃ᵗ mainly changes shadow size.

Deformation parameter ε₃ʳ affects shadow shape.

Some non-Kerr shadows have unique features for detection.

Abstract

We study the shadow of the Cardoso-Pani-Rico (CPR) black hole for different values of the black hole spin $a_*$, the deformation parameters $\epsilon_3^t$ and $\epsilon_3^r$, and the viewing angle $i$. We find that the main impact of the deformation parameter $\epsilon_3^t$ is the change of the size of the shadow, while the deformation parameter $\epsilon_3^r$ affects the shape of its boundary. In general, it is impossible to test the Kerr metric, because the shadow of a Kerr black hole can be reproduced quite well by a black hole with non-vanishing $\epsilon_3^t$ or $\epsilon_3^r$. Deviations from the Kerr geometry could be constrained in the presence of high quality data and in the favorable case of a black hole with high values of $a_*$ and $i$. However, the shadows of some black holes with non-vanishing $\epsilon_3^r$ present peculiar features and the possible detection of these shadows could unambiguously distinguish these objects from the standard Kerr black holes of general relativity.