Is it possible for photon to run in circle by its own gravity? I have heard that gravity came from energy and momentum so photon has gravity too.
Then there are theory state that photon has energy tied to frequency.
So if a photon has very very high frequency to the point that its gravity can affect normal photon and has a chance to bend its path slightly, it would get caught by its gravity, and maybe, it would run in looping path or circle.
Or if those kind of photon crossing each other it would trap each another and run in circle like two star swinging around.
I have guess that it actually exist and it maybe a fundamental particle we know.
Or not?
 A: If you consider your photon as a point object, it cannot bend its own path. It will always travel on the ridge it creates, speaking in terms of curvature of space. 
The other idea is possible. Two photons having a momentum, attract each other, trapping each other, like a positronium (typical example for this behavior). In the model of relativity this is possible. In reality there might be some problems. For example the radius of this bound state, might be larger than the size of our known universe. I don't know, but you can calculate it. If not, then the radius will still be very large, so the 2 photons need such empty space to get into this bound state, if there is other stuff to interact with, they will and won't fly around in circles. 
The other drawback might be, the frequency these photons need, might be so high, that it is in the regime of quantum foam. But in general relativity there is no h and no quantum foam. So at least on paper you can try to calculate a frequency that is high enough to trap another photon (like a black hole). 
Of course it will always be a theoretical idea, since you mix an object from quantum mechanics in a world of general relativity.
