Shadow of a naked singularity

Abstract

We analyze the redshift suffered by photons originating from an external source, traversing a collapsing dust cloud and finally being received by an asymptotic observer. In addition, we study the shadow that the collapsing cloud casts on the sky of the asymptotic observer. We find that the resulting redshift and properties of the shadow depend crucially on whether the final outcome of the complete gravitational collapse is a black hole or a naked singularity. In the black hole case, the shadow is due to the high redshift acquired by the photons as they approach the event horizon, implying that their energy is gradually redshifted toward zero within a few crossing times associated with the event horizon radius. In contrast to this, a naked singularity not only absorbs photons originating from the source, but it also emits infinitely redshifted photons with and without angular momenta. This emission introduces an abrupt cutoff in the frequency shift of the photons detected in directions close to the radial one, and it is responsible for the shadow masking the source in the naked singularity case. Furthermore, even though the shadow forms and begins to grow immediately after the observer crosses the Cauchy horizon, it takes many more crossing times than in the black hole case for the source to be occulted from the observer's eyes. We discuss possible implications of our results for testing the weak cosmic censorship hypothesis. Even though at late times the image of the source perceived by the observer looks the same in both cases, the dynamical formation of the shadow and the redshift images has distinct features and time scales in the black hole versus the naked singularity case. For stellar collapse, these time scales seem to be too short to be resolved with existing technology. However, our results may be relevant for the collapse of seeds leading to supermassive black holes.

26 pages, 11 figures

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• Can we distinguish black holes from naked singularities by the images of their accretion disks?
• Shadow of a Naked Singularity without Photon Sphere
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• Exploring light deflection and black hole shadows in Rastall theory with plasma effects
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• Shadows of Black Holes in Vector-Tensor Galileons Modified Gravity
• Fingerprints of the cosmological constant: Folds in the profiles of the axionic dark matter distribution in a dyon exterior
• Shadows of naked singularity in Brans-Dicke gravity
• Modelling the Sgr A${}^{\ast }$ and M87${}^{\ast }$ shadows by using the Kerr-Taub-NUT metrics in the presence of a scalar field
• The surface geometry and shadow of a Schwarzschild black hole with halo
• Sgr A* Shadow Study with KTN Space Time and Investigation of NUT Charge Existence
• Observational signatures of Rotating compact objects in Plasma space-time
• Shadow of higher dimensional collapsing dark star and blackhole
• A class of charged and charged-Taub-NUT metrics in the presence of a massless scalar field and some of their astrophysical aspects
• Cauchy horizon stability in a collapsing spherical dust cloud. II: Energy bounds for test fields and odd-parity gravitational perturbations
• Field Sources for Generalized Ellis-Bronnikov Wormhole