Theoretically proven based on Einstine's relativity study but scientifically not for there is no existing particle that can travel the same speed as the light even if it is increasingly accelerating. Well, not unless if it is a blackhole. :)
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It is more than just theoretical. I must disagree and confirm that black holes have somehow been experimentally observed.
The only way to generate the wave we observed comes from the collision of two black holes (or neutron stars). We have no other astrophysical object in our catalogue capable to be responsible for such observations. Of course, the observation could be due to something we don't know, but which mimics a black hole very very well (then let's call it a black hole in the meantime).
Concerning the speed of light, the neutron star events proved that gravitational waves travel at the speed of light, like photons and gluons by the way.
What about photons? They are zero mass particles that travel at the speed of light.
It represents a light so basically, it has similar features same as light and not more than the light can travel at 3x10^8 m/s. And also, particle must have mass enough to produce a certain amount of attracting force as it travels way beyond the speed of light. An object increases its mass as it travels a huge amount of speed say for example greater than light. Thus if it increases its mass then the force of attraction between anybody and that certain body increases.
The flaw here is that gravity does not involve only mass but also energy. In this way, photons are sensitive to gravity as well.
I guess I answered everywhere by now :)
Thanks for taking the time to clarify things!
It is always a pleasure! :)