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We show that the rotating generalization of Hayward's non-singular black holepreviously studied in the literature is geodesically incomplete, and that itsstraightforward extension leads to a singular spacetime. We present anotherextension, which is devoid of any curvature singularity. The obtained metricdepends on three parameters and, depending on their values, yields an eventhorizon or not. These two regimes, named respectively regular rotating Haywardblack hole and naked rotating wormhole, are studied both numerically andanalytically. In preparation for the upcoming results of the Event HorizonTelescope, the images of an accretion torus around Sgr A*, the supermassiveobject at the center of the Galaxy, are computed. These images contain, even inthe absence of a horizon, a central faint region which bears a resemblance tothe shadow of Kerr black holes and emphasizes the difficulty of claiming theexistence of an event horizon from the analysis of strong-field images. Thefrequencies of the co- and contra-rotating orbits at the innermost stablecircular orbit (ISCO) in this geometry are also computed, in the hope thatquasi-periodic oscillations may permit to compare this model with Kerr's blackhole on observational grounds.

Imaging a non-singular rotating black hole at the center of the Galaxy