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Context. The Event Horizon Telescope (EHT) collaboration recently obtainedfirst images of the surroundings of the supermassive compact object M87* at thecenter of the galaxy M87. Aims. We want to develop a simple analytic disk modelfor the accretion flow of M87*. Compared to general-relativisticmagnetohydrodynamic (GRMHD) models, it has the advantage of being independentof the turbulent character of the flow, and controlled by only feweasy-to-interpret, physically meaningful parameters. We want to use this modelto predict the image of M87* assuming that it is either a Kerr black hole, oran alternative compact object. Methods. We compute the synchrotron emissionfrom the disk model and propagate the resulting light rays to the far-awayobserver by means of relativistic ray tracing. Such computations are performedassuming different spacetimes (Kerr, Minkowski, non-rotating ultracompact star,rotating boson star or Lamy spinning wormhole). We perform numerical fits ofthese models to the EHT data. Results. We discuss the highly-lensed features ofKerr images and show that they are intrinsically linked to the accretion-flowproperties, and not only to gravitation. This fact is illustrated by the notionof secondary ring that we introduce. Our model of spinning Kerr black holepredicts mass and orientation consistent with the EHT interpretation. Thenon-Kerr images result in similar quality of the numerical fits and may appearvery similar to Kerr images, once blurred to the EHT resolution. This impliesthat a strong test of the Kerr spacetime may be out of reach with the currentdata. We notice that future developments of the EHT could alter this situation.Conclusions. Our results show the importance of studying alternatives to theKerr spacetime in order to be able to test the Kerr paradigm unambiguously.

Geometric modeling of M87* as a Kerr black hole or a non-Kerr compact object