Shadow of nulllike and timelike naked singularities without photon spheres

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In this paper, we derive general conditions for a shadow to occur, without a photon sphere in a spacetime, caused by central nulllike or timelike naked singularities.

• Using these conditions, we propose classes of spacetimes which have nulllike and timelike naked singularities at the center, and that fulfill these `shadow without photon sphere' conditions.
• Considering additional asymptotically flat conditions, we show that, for a fixed Schwarzschild mass, the timelike naked singularities can cast a shadow of a size that is equal to, greater or smaller, than the size of a black hole shadow.
• On the other hand, the size of shadow of a nulllike naked singularity is always less than that of a black hole.