In the case of black holes, lights are pulled into by great gravitational force exerted by the dying stars (which forms into a black hole). If light has no mass, how is light affected by gravity?
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Fun titbit: we actually don’t know for sure that photons have no mass! I don’t think they have mass, and hear me out before you down-vote this post for being “clearly wrong”:
First off, we indeed have no good reason to expect photons to have any rest mass and Occam’s razor thus suggests to believe they really do not have any. Massless means always moving at the speed of “light”, but in the Theory of Relativity c is actually the speed of causality (and gravity, but that is a similar can of worms). Conversely, having mass means to never be able to move at full c.
Actual real light _could_ always be slower and it is in many cases such as in a medium, for example air or glass; that’s why c is _at best_ the speed of light _in vacuum_.
But what if photons have an extremely tiny rest mass after all? Would physics break? Actually not, things just become much more ugly and complicated (see below). But reality ultimately doesn’t care about our beauty standards.
We actually other particles that by our best guesses _should_ have a rest mass, yet so far we never saw any, nor were we able to measure any difference between c and the speed they move at: neutrinos. Or rather, at least two of the three neutrino types. We know this, assuming our physical understanding, because they can turn into each other over time (called “neutrino oscillation”), and this implies that the three types must have different rest masses. Hence at most one of them can have none, the others must have some!
As said above, this is the only proper evidence for neutrinos having any mass at all, other attempts to find a difference have failed. So could the same be true with photons after all? Might we just not have found the proper experiment that shows they also must have mass? There are even other examples of numbers in physics that _seem_ to be exactly 0, but beyond it being really, really neat, we have no confirmation.
What our experiments show is that the mass of photons, if any, is absurdly small. We can find bounds on it in many ways, from direct measurements to theoretical predictions such as the maximal range of electromagnetism: the range of a force is limited by the particles it acts with, _exchange particles_, and only massless ones allow infinite range; that’s why the nuclear forces only act in small distances, the respective particles have mass, while photons are the exchange particle of electromagnetism. Yet we can only measure speed to some precision and electromagnetism only is confirmed to act within millions of light years. Even if it acts over many billions of light years that is still not enough to confirm true infinities.
People also often say that this or that implies that light _must_ move at c in vacuum. But those statements are always based on theories that have this as a basic assumption, an axiom, to begin with! (Interestingly, the theory of relativity does not truly need this assumption.)
When googling for such arguments (try it!) one finds fancy-sounding argument involving words such as “gauge invariance” (that is a hard one to explain properly, so I will just blackbox it), and indeed the latter would ultimately only work properly if photons are massless. But maybe… we are wrong and there is no “gauge invariance”?
Physics can be adapted to work with a mass-y photon. As said, it would just be much more ugly by our standards. Most things should remain unchanged, at least within any measurable approximations.
So, should we really think light moves slower than c, and photons have rest mass? No, most likely not. Multiple meta-physical reasons such as Occam’s razor tell us to assume the simpler theory, which clearly is massless photons. But it also tells us to always keep an eye out for the small chance that this assumption(!) is wrong.
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