Question: We all agree that light has no mass yet it is affected by gravity. According to accepted theories I have seen light itself is also said to bend space meaning that it causes gravitation. This would seem to contradict the very definition of gravity as an attractive force between two masses. It also seems to cause contradiction as the energy of light varies depending on the observer.
I have heard of a phenomena called Gravitomagnetism which is said to be an analog to magnetism. As I understand it, this is a force which pull masses in the direction of other masses that pass by similar to how magnetism pull charges in the direction (or opposite direction) of electrical current.
So my question is this - does light in fact have gravity or does it just have Gravitomagnetism meaning the ability to pull nearby object in its direction of travel rather than toward the light-beam.

Answer: 
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> So my question is this - does light in fact have gravity or does it just have Gravitomagnetism meaning the ability to pull nearby object in its direction of travel rather than toward the light-beam.
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Here is a list of the abilities that light has, and after each ability in parenthesis there is the name of the ability.

1. Light has the ability to pull a nearby massive object towards itself. (attractive gravity)
2. Light has the ability to pull a nearby massive object in its direction of travel. (gravitomagnetic induction a.k.a frame dragging)
3. Light has the ability to not pull nearby parallel light towards itself. (attractive gravity and repulsive gravitomagnetism together)
4. Light has the ability to pull nearby anti-parallel light towards itself. (attractive gravity and attractive gravitomagnetism together)
5. Finally, I think two passing anti-parallel light pulses should induce some gravito-motive forces on each other, but after they have passed they should be like before the passing, except for some small change of direction. Like two passing electrons induce an electro-motive force on each other.
“Gravitomagnetism” is just one formalism for understanding General Relativity. In GR, the density *and flow* of energy *and momentum* (expressed as the [energy-momentum-stress tensor](https://en.wikipedia.org/wiki/Stress%E2%80%93energy_tensor)) is what causes spacetime curvature and affects the motion of particles. Whether you are talking about massive or massless particles, their motion helps determine the gravity they cause.

If you want to see how the velocities and accelerations of two massive particles affects their mutual gravitational accelerations, look at the [Einstein-Infeld-Hoffmann equations](https://en.wikipedia.org/wiki/Einstein%E2%80%93Infeld%E2%80%93Hoffmann_equations). I have not seen analogous equations for massless particles, but they probably exist.