The images of Brans-Dicke-Kerr type naked singularities

TL;DR

This paper investigates the images of Brans-Dicke-Kerr spacetimes, revealing unique shadow structures and fractal features that could help distinguish these naked singularities from other black hole solutions, aiding future tests of Brans-Dicke theory.

Contribution

It provides the first detailed analysis of the optical appearance of Brans-Dicke-Kerr naked singularities, highlighting how their images differ from Kerr black holes based on the Brans-Dicke parameter.

Findings

Shadows become flatter and smaller as  decreases for   M.

Shadow shapes include a 'jellyfish' pattern with fractal structures when <1/2.

Distinct gray regions appear for  > M, differentiating from Kerr solutions.

Abstract

We have studied the images of the Brans-Dicke-Kerr spacetime with a dimensionless Brans-Dicke parameter $\omega$, which belongs to axisymmetric rotating solutions in the Brans-Dicke theory. Our results show that the Brans-Dicke-Kerr spacetime with the parameter $\omega>-3/2$ represents naked singularities with distinct structures. For the case with $a \leq M$, the shadow in the Brans-Dicke-Kerr spacetime persists, gradually becomes flatter and smaller as $\omega$ decreases. Especially when $\omega<1/2$, the shadow in the image exhibit a very special ``jellyfish" shape and possesses a self-similar fractal structure. For the case with $a > M$, a distinct gray region consisting of two separate patches appears in the image observed by equatorial observers. This indicating that the Brans-Dicke-Kerr spacetime can be distinguished from the Kerr and Kerr-de Sitter cases based on its image. These effects of the Brans-Dicke parameter could help us to reveal the intrinsic structure of the Brans-Dicke-Kerr spacetimes and provide a foundation for testing Brans-Dicke theory through future high-precision observations.