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If photons are massless, why does light get attracted to black holes?

Photons have no rest mass. But the quantity that determines how a thing gravitates, or responds to gravitation, is not rest mass. It is a complex entity called the stress-energy-momentum tensor that consists of energy, momentum, pressure and shear stresses. (It is usually represented by a 4 times 4 symmetric matrix. It is not a simple number.) Now it so happens that for most everyday objects, their speeds are small compared to the speed of light, and pressure and stresses are also small compared to relativistic mediums. So the stress-energy-momentum tensor is dominated by rest mass. When it comes to the Sun, the Earth, a lump of metal, a human being… gravitational behavior is very accurately (but not perfectly!) described using Newtonian gravity and their respective rest masses. But the moment we get to relativistic speeds, this is no longer the case. Entities can no longer be characterized by rest mass alone; other components of the tensor become equally important. In particular, a ph...