Could Gravi Balls Provide Evidence for Graviton Theory?

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The discussion explores the concept of "Gravi Balls," hypothetical bound states of gravitons, analogous to glue balls formed by gluons in the chromoelectric field. It suggests that since gravity acts on mass-energy, the gravitational field should theoretically interact with itself, potentially leading to the formation of these Gravi Balls. However, it is noted that the existence of Gravi Balls is highly unlikely, as gravitons would behave more like photons than gluons. The comparison highlights that while both electromagnetic and gravitational forces follow inverse square laws, gluons operate differently. The idea raises questions about the search for evidence supporting or refuting graviton theory using particle accelerators.
MathNerd
The chromoelectric field, which acts on the color charge, is attributed to the strong nuclear force. Discrete quanta of this field are called gluons, gluons also have a color charge. Therefore the chromoelectric field interacts with itself and it can form tiny bundles of gluons that form bound states and we call these glue balls.

My question is that seeing as gravity acts on mass-energy and gravitons have energy then the gravitational field should interact with itself and like the chromoelectric field it should form little bundles of gravitons in bound states, I call these “Gravi Balls”. Couldn’t we look for “Gravi Balls” with particle accelerators to try to support or refute the graviton theory?
 
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Gravi balls are hihly unlikey. Gravitons would resemble photons a lot more closely than gluons. For example electromagnetic force (mediated by photons)and gravity (mediated by gravitons) both have inverse square laes. Gluons are quite different in this respect.
 
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