Does Komar Mass Include the Energy of Gravitational Field?

[wLw]

In Newtonian physics $\rho$ only includes "matter mass". But that is also true in General Relativity. Look at the Komar mass integral again: the "binding energy" factor is not $\rho$ (or more generally $\rho + 3p$, which is the "source" factor that comes from the matter). If you have to pick a particular factor in the integral that represents "binding energy", it would be $\sqrt{g_{tt}}$, the redshift factor. But really "binding energy" is not localized at all; it's a global property of the system--it's the fact that the mass $M$ of the bound system is less than the total mass of all the constituents would be if they were all widely separated from each other.

so the gravitational radiation refers to the energy of outside gravitational filed (generated by body), and the gravitational (no filed ,because it is binding energy)energy in komar mass is binding energy，but both of them are nonlocalizable?,is i right.?

 

[PeterDonis]

so the gravitational radiation refers to the energy of outside gravitational filed (generated by body), and the gravitational (no filed ,because it is binding energy)energy in komar mass is binding energy，but both of them are nonlocalizable?,is i right.?

You are trying to use terminology that is not very suitable. In particular, you are continuing to cling to the concept of "energy of the gravitational field", which is not a good concept. It doesn't help with understanding; it hinders it.

Gravitational waves carry energy because they can do work. For example, if they pass through an object they will heat it up (by a very small amount, but the effect is there). But the waves' ability to do work is not localizable.

Gravitational binding energy of a bound object is there because, in order to take a system consisting of a lot of small, widely separated pieces of matter, and make them into a single bound object like a planet, you need to extract energy from the system (the usual way this happens is for the system to emit electromagnetic radiation that escapes to infinity); or, conversely, if you want to take a single bound object like a planet and make it into a lot of small, widely separated pieces of matter, you need to add energy to (do work on) the system. But, again, this property of the system is not localizable; the transition I just described, in either direction, is a global operation.

I have just described the actual physics of gravitational waves and gravitational binding energy. Using the term "energy of the gravitational field" adds nothing at all to the physics, nor does it help to understand the physics I have described. The best thing you can do is to just forget about the concept altogether and focus on the actual physics.

 

[wLw]

ok thank you a lot, i am clearer than before

 

[PeterDonis]

thank you a lot

You're welcome!