The photon and gravity paradox, a thought experiment. is it possible?

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So what is the deal with photons (light waves) being massless and gravity’s ability to only have an effect on a particle of mass?

The Paradox - a photon is a particle of no mass, and gravity can only affect mass. It exerts it’s pull or tug on particles containing mass. That being the case then how is it, that light is affected by gravity?

If light is affected by gravity then that infers a photon has mass, correct? But if a photon has mass and it’s moving at c it should then be infinitely massive, as physics details. As we all know an infinite mass equals a singularity or black hole.

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