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 ω, which belongs to axisymmetric rotating solutions in the Brans-Dicke theory. Our results show that the Brans-Dicke-Kerr spacetime with the parameter ω>-3/2 represents naked singularities with distinct structures. For the case with a ≤ M, the shadow in the Brans-Dicke-Kerr spacetime persists, gradually becomes flatter and smaller as ω decreases. Especially when ω<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.
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