The images of a rotating naked singularity with a complete photon sphere

For a black hole, the appearance of a shadow is due to the light rays entering the event horizon, and the unstable photon sphere determines the boundary of shadow. Our research indicates that even in the presence of a complete photon sphere without an event horizon, a shadow will not be formed. We present the images of Konoplya-Zhidenko compact object with or without complete photon sphere, and investigate the influence of unstable photon circular orbits (UPCOs) and stable photon circular orbits (SPCOs) on the images of Konoplya-Zhidenko compact object. When the event horizon is absent, the unstable prograde and retrograde light rings can also exist, so dose the complete photon sphere. But the dark shadow doesn’t emerge, and the image of the complete photon sphere appears as an infinite number of relativistic Einstein rings. For this case, the light rays pass through the photon sphere, but eventually escape to infinity. For some parameter values, only the unstable retrograde light ring can exist, which leads to an incomplete photon sphere. In this case, the dark shadow also doesn’t emerge, and the image of the incomplete photon sphere appears as an infinite number of relativistic Einstein arcs. Furthermore, in Konoplya-Zhidenko naked singularity spacetime, the stable LRs and SPCOs can also exist, but they have no effect on the naked singularity image. This study may contribute to future astronomical observations, and aid in verifying the cosmic censorship conjecture and various gravitational theories.

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