Gravitational waves and gravitation

[Ranku]

Gravitational waves are generated when the mass quadrupole moment changes in time.
We also know motion of mass contributes to its gravitation. Does the producing process of gravitational waves, which involves mass in accelerated motion, produce gravitation as well? If so, is it of less, equal or more magnitude than the gravitational waves being generated?

 

[Jonathan Scott]

Gravitational waves are generated when the mass quadrupole moment changes in time.
We also know motion of mass contributes to its gravitation. Does the producing process of gravitational waves, which involves mass in accelerated motion, produce gravitation as well? If so, is it of less, equal or more magnitude than the gravitational waves being generated?

Firstly, this question is a bit mixed up, as "gravitation" is normally considered to mean a gravitational field, but strength of gravitational waves is related to the rate of change of the gravitational field, so these quantities cannot be compared.

Secondly, you can't move or accelerate a mass in isolation (the center of mass of any complete system moves with constant velocity), so for example you can't cause the gravitational field of a system to change abruptly by pushing it sideways, because the gravitational field of the pushing mechanism will cancel out the change to first order.

The best you can do is to change the distribution of mass, creating tidal effects, plus gravitational waves if you do it fast enough.

 

[Ranku]

Firstly, this question is a bit mixed up, as "gravitation" is normally considered to mean a gravitational field, but strength of gravitational waves is related to the rate of change of the gravitational field, so these quantities cannot be compared.

Secondly, you can't move or accelerate a mass in isolation (the center of mass of any complete system moves with constant velocity), so for example you can't cause the gravitational field of a system to change abruptly by pushing it sideways, because the gravitational field of the pushing mechanism will cancel out the change to first order.

The best you can do is to change the distribution of mass, creating tidal effects, plus gravitational waves if you do it fast enough.

Ok, let me put it in a quantum mechanical way. Gravity waves are real gravitons. Gravity is virtual gravitons. Does any process that produces real gravitons also produce virtual gravitons?

 

[bcrowell]

Gravitational waves are generated when the mass quadrupole moment changes in time.
We also know motion of mass contributes to its gravitation. Does the producing process of gravitational waves, which involves mass in accelerated motion, produce gravitation as well? If so, is it of less, equal or more magnitude than the gravitational waves being generated?

For concreteness, let's imagine a system consisting of two objects of mass m, in circular orbits of radius r about their common center of mass. The power radiated in gravitational waves scales like $(m/r)^5$. The kinetic energy and binding energy of the system scale like $m^2/r$. Although this is an apples-and-oranges comparison (power versus energy), I think it should be pretty clear that the two effects scale differently, so there is no particular reason to expect them to be on the same order of magnitude. To do more of an apples-to-apples comparison, you'd probably want to consider some measure of tidal forces (e.g., the Weyl tensor) at some distance from the system. In realistic observations, we wouldn't even use the same apparatus to try to detect both effects. For a system whose gravitational waves we might hope to be able to detect, we would be looking for an AC component of the tidal forces, whereas any DC component of such a system would be masked by the presence of all the other masses in our galaxy.

 

[Ranku]

For concreteness, let's imagine a system consisting of two objects of mass m, in circular orbits of radius r about their common center of mass. The power radiated in gravitational waves scales like $(m/r)^5$. The kinetic energy and binding energy of the system scale like $m^2/r$. Although this is an apples-and-oranges comparison (power versus energy), I think it should be pretty clear that the two effects scale differently, so there is no particular reason to expect them to be on the same order of magnitude. To do more of an apples-to-apples comparison, you'd probably want to consider some measure of tidal forces (e.g., the Weyl tensor) at some distance from the system. In realistic observations, we wouldn't even use the same apparatus to try to detect both effects. For a system whose gravitational waves we might hope to be able to detect, we would be looking for an AC component of the tidal forces, whereas any DC component of such a system would be masked by the presence of all the other masses in our galaxy.

So what is meaning of "AC" and "DC" components of tidal force?

Also, can you answer the gravity waves question quantum mechanically: Gravity waves are real gravitons. Gravity is virtual gravitons. Does the process that produces real gravitons also produce virtual gravitons?

 

[bcrowell]

So what is meaning of "AC" and "DC" components of tidal force?

The same as for an electric current:the oscillating and non-oscillating terms in the Fourier spectrum.