Cosmic Censorship in Sgr A* and M87*: Observationally Excluding Naked Singularities

Abstract The imaging of Sagittarius A* (Sgr A*) and the supermassive black hole at the center of Messier 87 (M87*) by the Event Horizon Telescope constrains the location and nature of emission from these objects. Coupled with flux limits from the near-infrared through the ultraviolet, the attendant size constraints provide strong evidence for the absence of an accretion-powered photosphere, and therefore for the existence of an event horizon about an astrophysical black hole. Here, we demonstrate that a broad class of naked singularities exhibit inner turning points for time-like geodesics, and therefore may generically be excluded, regardless of the nature and unknown physical impact of the singularity itself, subject to the single weak assumption that its nongravitational impact is localized to its immediate vicinity. While we restrict our attention to static, spherically symmetric spacetimes, we are nevertheless able to exclude or constrain a large number of commonly invoked naked singularity spacetimes in this way.