Both energy and mass gives has gravity. If an object receives energy, it will appear heavier and space will curve slightly more around that object.
That energy could be potential energy, or static energy.
If an object A is accelerated toward a black hole B, it gains velocity and thus energy. It will probably not observe that increase in energy locally, but a distant observer C should see an increase in gravity from that object as it gains kinetic energy. Since the black hole B also is accelerated in the opposite direction, observer C should ALSO observe an increase in gravity from the black hole.
From this I assert that:
A pair of distant objects should amplify each others gravity when observed by a third party.
Object A will see an increase in gravity from B as it comes closer to B and vice versa, meaning that Newtons formula should be off by a tiny margin.
Observer C would assume objects A and B are heavier than they actually are when observed from A or B. Observer C would the use "wrong" numbers to calculate other nearby objects trajectories etc.
Would observer C also actually SEE different trajectories in assertion 3? It seems illogical that we'd see an asteroid collide into the surface of a planet, while it didn't collide from a different frame of reference due to them not observing the same increase in kinetic energy...
Clarification:
It is my understanding the gravity around an object increases as it is given more energy. The amount of kinetic energy an object has, is relative to the observer.
Example: Two exoplanets are moving in opposite directions. Between them they will have a lot of kinetic energy. Planet 1 then passes near a star, and its trajectory and velocity changes so that it is parallel to the trajectory and velocity of planet 2.
Between planets 1 and 2, there is no longer any kinetic energy.
Then an asteroid comes close to planet 1. From earth, we see planet 1 having a certain mass and a certain energy level - and both of those factors affect the trajectory of the asteroid. The new trajectory we observe for the asteroid means that the asteroid will collide with our moon.
Observed from planet 2, planet 1 does not have the same energy level. It still has the same mass. So planet 2 then sees the asteroid getting a different trajectory, and sees it actually hitting earth instead of the moon.
The question is: what would observers on planet 2 and earth actually see? Which photons would reach them?
Could it in some way be so that observers on planet 2 actually see a devastation on earth? Sounds like a paradox to me.
