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arXiv · 2511.01478

The images of Brans-Dicke-Kerr type naked singularities

Fen Long·Weike Deng·Xin Qin·Songbai Chen·Jiliang Jing
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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.

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Fen Long, Weike Deng, Xin Qin, Songbai Chen, Jiliang Jing. 2025-11-03. The images of Brans-Dicke-Kerr type naked singularities. https://arxiv.org/abs/2511.01478

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