Why are massless photons affected by gravity?

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In general relativity, gravitation is a manifestation of the curvature of spacetime. The motion of all objects is affected by this curvature, regardless of whether they have mass or not. Light follows geodesic paths in spacetime, which are straight lines in flat spacetime, and curved paths in curved spacetime.

Note that by "mass" above I mean "invariant mass" as discussed in the following FAQ:

https://www.physicsforums.com/showthread.php?t=511175 [Broken]

because it is the invariant mass that is zero for a photon. If you prefer to think in terms of "relativistic mass" (which is related to energy via [itex]E = m_{rel} c^2[/itex], note that all photons (as far as we know) follow the same geodesics, regardless of their energy. This has been verified, for example, by comparing the deflection of visible light as it passes close to the sun, with the deflection of radio waves from distant sources.

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In general relativity, gravitation is a manifestation of the curvature of spacetime. The motion of all objects is affected by this curvature, regardless of whether they have mass or not.
So, in GR there are no attractive forces between two masses?
 
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Mass produces spacetime curvature (as do energy and momentum), so two masses affect each other gravitationally. Whether to call this "force" is a matter of semantics. If you are falling freely under only the influence of gravity, you do not "feel" it, unless the curvature is so strong as to produce tidal stresses in your body. Therefore many people do say that "gravity is not a force."
 
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