The images of Brans-Dicke-Kerr type naked singularities

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 $a\le M$, 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.

15 pages, 8 figures It is to be published in Chinese Physics C