I was told that photons have no (rest) mass. However I thought that black holes are called "black" because no light can go escape the gravity force in their vicinity. I somehow think that, if light is just photons, then it should not be affected by gravity. Hence black holes could catch everything but light.
Do I miss something? Is light more than a bunch of photons? Or maybe black holes are not exactly what I think.
A massive object like a black hole bends space-time in a "singular" way. But it is not necessary to look at black holes to observe phenomena that can affect the trajectory of light. Through the gravitational lens effect, stars that are "behind" galaxies can be spotted from Earth because their light is being bent by the gravitational effects of the galaxy in between the star and Earth. Getting back to the "mechanics" of general relativity, light travels on geodesics, which are determined by the geometry of space-time. The latter is in turn determined by the matter distribution across the universe. Around massive black holes, the idea of straight line, which is a special instance of geodesics in flat space, changes to a curved trajectory. So one can say that light is still travelling on a straight line, only problem is that this straight line is deformed by the mass distribution around it.
To make sense of why light is also affected by gravity one can argue that general relativity is an "extension" of special relativity, where mass and energy can be thought of being the same thing up to a fixed "exchange rate" given by the speed of light in the vacuum: $E=mc^2$. Photons don't have mass, but they do have energy according to $E = h\nu$, where $\nu$ is the frequency of the observed light. Indeed energy is one of the 10 components of the (symmetric) energy-stress tensor that figures in Einstein's fields equations for the geometry of space-time.
With gravity we notice that everything is affected in a way independent of the mass. A light object and a massive object with the same velocity move the same under gravity. And the motion is one to converge lines together (if everything is drawn towards the center of the earth, they are drawn together). A curved spacetime does exactly that, just like all paths from the north pole converge on the south pole, if we have a curved spacetime then everything can converge due to curvature, regardless of whether it is light or heavy.
Once everything moves that way regardless of mass, then light itself is forced to so itself. The spacetime outside a black hole is curved, so that affects the light outside a black hole. The curvature outside the black hole was fixed by the matter than collapsed in to form the black hole, and it set up curvature that begets equal curvature, that persists in time. For an event horizon, those paths (that work just as well regardless of the mass of the thing following them) don't get any farther away from the black hole, so nothing (not even light) can escape because everything is affected in away independent of how much mas it has.
