There is something that has been bothering me for some time about binding energy (and respective mass difference) but I was not sure how to formulate the question. Now it feels like I can ask it meaningfully enough.(adsbygoogle = window.adsbygoogle || []).push({});

In GR energy produces gravity just like mass. But how potential energy is accounted for in GR?

To illustrate my reasoning I will use scenario and it is supposed to be weak field limit so that concepts of Newtonian gravity are meaningful enough.

Lets say we have configuration of objects that are bound by being in potential well of gravity. We add from outside some energy ##E_o##. So the mass of the configuration as seen form outside has increased by the amount ##m=\frac{E_o}{c^2}##. According to virial theorem twice that amount of kinetic energy of the configuration will be converted into potential energy of configuration. Now if we compare theoretical "inside" descriptions of two configurations, mass of the objects stay the same while at the same time the kinetic energy has been reduced by amount ##E_o##. So to get the correct change in mass as seen from outside we have to add the difference in potential energy too.

So how this mass increase due to potential energy shows up in GR formalism?

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# I Mass of potential energy in GR

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