Light wave with gravitational component It may sound a little naive but... Is it possible for a light wave to have a gravitational wave component?
 A: There is a fairly small number of known exact solutions to general relativity.
One of them is the so called monochromatic electromagnetic plane wave where the Stress-Energy of the electromagnetic wave is a source of gravity and there is a gravitational wave and an electromagnetic wave and the gravitational wave and the electromagnetic wave travel together.
It satisfies the Maxwell and the Einstein equations so the fields and the metric coevolve together so that Maxwell, and the metric, tell the electromagnetic field how to evolve and the Stress-Energy tensor of the electromagnetic field, and Einstein, tell the metric field how to evolve. And the things they evolve into are exactly what they are and they evolve together in a consistent fashion.
It's one of a few known electrovacuum solutions to the Einstein-Maxwell system.
A: When and if all fundamental forces are unified which happens at very high energies, imagined only for cosmological models, all gauge bosons become massless and transfer a unified "force". In that sense it should be possible that the "light waves" build up by the confluence of the elementary fields of photon, gluon, W and Z and gravitons might ( in some model) carry all four fundamental components with some percentage.  No wonder it is called primordial soup.
