A question about light and gravity

First off, just to check that I'm right with these two statements.
1. Light is a wave and has no mass and no physical prescence.
2. The force of gravity is an attractive force between two physical bodies that both have mass.

So if they're both true, how come light gets sucked in by black holes? If light has no physical mass, then it shouldn't be affected by gravity at all, no matter how massive. Have I made a mistake somewhere?

Light is both a massless particle and a wave, hence wave particle duality.

for those of you that have commented about wave particle duality, this is not the reason for light being effected by gravitation.

The way you can describe why light goes into a black hole is simple, if you use relativity. This is a short description:

Relativity determines that the whole of space-time can be warped and curved by gravity, according to Einstien, gravity is not a force as such, it is a result of the motion of objects. As space time dips where there is mass you could imagine it like a bowling ball on a mattress, you would notice that the mattress has been dipped, and if you where to put a marble on the mattress, it would travel towards the bowling ball. From our perspective - very close up - we can see that the two objects have no physical attraction too each other, but if you are too zoom out, or make the mattress invisible, what you see is a marble mysteriously moving towards a bowling ball. In a similar way, objects on the space time continuum distort space time and cause the objects to 'fall' towards them (this falling is as a result of the principle that all objects travel along the shortest path of space time - and you may argue that if this were so, stationary objects would not be affected, but you have to remember that all things have motion through time, even light.) So although light has no mass, it is still required to follow the shortest path in space time.