Abstract <p>The appearance of a shadow (a dark spot in the vicinity of a black hole) was first considered in a thought experiment by James Bardeen in 1973. However, he did not discuss the possibility of astronomical observations of the shadow, since its size was too small for all known estimates of black hole masses and distances to them. In addition, Bardeen’s assumption of a luminous screen behind the black hole seemed unrealistic. In 2005, we predicted that if we observe a supermassive black hole in the Galactic Center in the mm- or submillimeter range, we will be able to detect a dark spot (shadow) with a size (diameter) of approximately 50 angular µs (µas) (since, as indicated in the text of the cited paper, <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11496_2025_8974_Article_IEq1.gif" Format="GIF" Height="18" Rendition="HTML" Resolution="72" Type="Linedraw" Width="53" /> </InlineMediaObject> <EquationSource Format="TEX">\({{r}_{{\text{g}}}} = 10\)</EquationSource>  </InlineEquation> µas for the black hole in the Galactic Center, while the size of the shadow is <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11496_2025_8974_Article_IEq2.gif" Format="GIF" Height="24" Rendition="HTML" Resolution="72" Type="Linedraw" Width="62" /> </InlineMediaObject> <EquationSource Format="TEX">\({{(27)}^{{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}}}}{{r}_{{\text{g}}}}\)</EquationSource>  </InlineEquation>). This prediction was confirmed in 2022 after processing the observations of the Galactic Center obtained by the Event Horizon Telescope Collaboration (the corresponding observations were conducted in 2017). Previously, we obtained analytical relationships for the size of the shadow both for the Reissner—Nordström black holes with an electric charge and with a tidal charge, which can arise due to the presence of an additional dimension. Thus, it proves to be possible to limit the charges (including tidal ones) for Sgr A* and М87* based on the shadow sizes obtained from observations in the vicinity of these objects. The issues concerning the presence of shadows in the vicinity of naked singularities and wormholes are discussed.</p>

Shadows of Galactic Centers: from Supermassive Black Holes to Naked Singularities and Wormholes

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发表日期：

2025年4月1日

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A. F. Zakharov

摘要

Abstract

The appearance of a shadow (a dark spot in the vicinity of a black hole) was first considered in a thought experiment by James Bardeen in 1973. However, he did not discuss the possibility of astronomical observations of the shadow, since its size was too small for all known estimates of black hole masses and distances to them. In addition, Bardeen’s assumption of a luminous screen behind the black hole seemed unrealistic. In 2005, we predicted that if we observe a supermassive black hole in the Galactic Center in the mm- or submillimeter range, we will be able to detect a dark spot (shadow) with a size (diameter) of approximately 50 angular µs (µas) (since, as indicated in the text of the cited paper, \({{r}_{{\text{g}}}} = 10\) µas for the black hole in the Galactic Center, while the size of the shadow is \({{(27)}^{{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}}}}{{r}_{{\text{g}}}}\) ). This prediction was confirmed in 2022 after processing the observations of the Galactic Center obtained by the Event Horizon Telescope Collaboration (the corresponding observations were conducted in 2017). Previously, we obtained analytical relationships for the size of the shadow both for the Reissner—Nordström black holes with an electric charge and with a tidal charge, which can arise due to the presence of an additional dimension. Thus, it proves to be possible to limit the charges (including tidal ones) for Sgr A* and М87* based on the shadow sizes obtained from observations in the vicinity of these objects. The issues concerning the presence of shadows in the vicinity of naked singularities and wormholes are discussed.