Lensing by a Fisher-Janis-Newman-Winicour naked singularity: Observational issues related to the existence of caustic bending in the strongly scalarized case

One reconsiders strong lensing by the naked singularity that enters the Fisher/Janis-Newman-Winicour (F/JNW) scalar-tensor spacetime, characterized by a mass $m$ and a scalar parameter $b$. One mainly focuses on the strongly scalarized case where the bending of light experiments a maximum value, resulting in the formation of a $b$ dependent caustic cone. One numerically determines the caustic cone's aperture $b$ dependence profile, and shows that this cone results in a flare sequence if the singularity is orbited by a star having an orbital inclination that satisfies a simple $b$ dependent condition. Such flare sequences qualitatively distinguish such F/JNW spacetimes from the usual black hole case. One then investigates the scenario that replaces the black hole located at the center of our Galaxy by a strongly scalarized F/JNW singularity having the same mass $m$. One shows that if a sequence of flares associated to the motion of a star orbiting not too far from the singularity (for the usual perihelion precession to have measurable effects) is detected, this would not only be an argument in favor of the presence of a (strongly scalarized) naked singularity with respect to the usual black hole assumption, but it could also return constraints on $b$ and determine the star's orbital parameters, even if the star can not be monitored directly.

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