Orbital period decay and gravitational waves

[Ranku]

We know that the orbital period of binary stars decay due to the emission of gravity waves that carry away energy from the system. What is the form of the energy loss of the system: kinetic energy or potential energy?

 

[bcrowell]

The classification of energy as kinetic or potential isn't valid in general relativity. There's a nice detailed discussion of this, at a fairly elementary level, in Exploring Black Holes by Taylor and Wheeler. For a more technical discussion, see http://nedwww.ipac.caltech.edu/level5/March01/Carroll3/Carroll6.html . Due to the equivalence principle, it isn't even possible to assign a definite energy density to the gravitational field, but you can sort of do it if you average over many wavelengths.

 

[Ranku]

The classification of energy as kinetic or potential isn't valid in general relativity. There's a nice detailed discussion of this, at a fairly elementary level, in Exploring Black Holes by Taylor and Wheeler. For a more technical discussion, see http://nedwww.ipac.caltech.edu/level5/March01/Carroll3/Carroll6.html . Due to the equivalence principle, it isn't even possible to assign a definite energy density to the gravitational field, but you can sort of do it if you average over many wavelengths.

So we simply have to refer to energy involved in an orbit as orbital energy. Is it not possible to be any more specific than that?

Also, why are gravity waves called as such, when they do not have a gravitational source (the source is a time varying mass quadrupole moment) or any gravitational effect?

 

[bcrowell]

So we simply have to refer to energy involved in an orbit as orbital energy. Is it not possible to be any more specific than that?

Right.

Also, why are gravity waves called as such, when they do not have a gravitational source (the source is a time varying mass quadrupole moment) or any gravitational effect?

I would say that a mass is a gravitational source, and that spacetime curvature is a gravitational effect.

 

[Ranku]

I would say that a mass is a gravitational source, and that spacetime curvature is a gravitational effect.

But the effect of gravitational waves on an object is not gravitational. In a dust sphere it causes non-gravitational tidal acceleration. And primordial gravitational waves may actually be repulsive!http://arxiv.org/abs/0909.1922v1

 

[bcrowell]

But the effect of gravitational waves on an object is not gravitational. In a dust sphere it causes non-gravitational tidal acceleration. And primordial gravitational waves may actually be repulsive!http://arxiv.org/abs/0909.1922v1

Tidal accelerations are gravitational accelerations.

 

[Ranku]

Tidal accelerations are gravitational accelerations.

Right. What I was trying to get at is, while gravitation causes attraction of the mass as a whole, as well as tidal effects, gravitational waves cause only tidal acceleration, and there is no attraction of the mass as a whole toward the source of the gravitational waves.

Now, when a mass changes shape or position, the change in the gravitational field is communicated across spacetime through gravity waves. However, not all changes in shape or position of mass generates gravity waves. How is the change in gravitational field communicated then?

 

[bcrowell]

Right. What I was trying to get at is, while gravitation causes attraction of the mass as a whole, as well as tidal effects, gravitational waves cause only tidal acceleration, and there is no attraction of the mass as a whole toward the source of the gravitational waves.

That's true.

Now, when a mass changes shape or position, the change in the gravitational field is communicated across spacetime through gravity waves. However, not all changes in shape or position of mass generates gravity waves. How is the change in gravitational field communicated then?

If the distant field changes, the change is always transmitted through a gravitational wave. You could have cases where the distant field doesn't change at all, e.g., a spherically symmetric mass distribution that changes while remaining spherically symmetric.

 

[Ranku]

If the distant field changes, the change is always transmitted through a gravitational wave. You could have cases where the distant field doesn't change at all, e.g., a spherically symmetric mass distribution that changes while remaining spherically symmetric.

Suppose this spherical mass contracts, and because of increased density its gravitational field becomes stronger. But we know by Birkhoff's theorem this contraction will not produce gravity waves. How then is the change in the strength of its gravitational field communicated?

 

[bcrowell]

Suppose this spherical mass contracts, and because of increased density its gravitational field becomes stronger.

It doesn't.

 

[Ranku]

It doesn't.

Oh. Wouldn't a star that has gravitationally collapsed to a neutron star or black hole have a stronger gravitational field than it did before when it was a star?

 

[Parlyne]

Oh. Wouldn't a star that has gravitationally collapsed to a neutron star or black hole have a stronger gravitational field than it did before when it was a star?

Not as measured outside the surface of the pre-collapse star.

 

[bcrowell]

To amplify on what Parlyne said, this isn't really anything about relativity; it's something you can understand in the context of Newtonian mechanics: http://en.wikipedia.org/wiki/Shell_theorem

 

[Ranku]

Not as measured outside the surface of the pre-collapse star.

To amplify on what Parlyne said, this isn't really anything about relativity; it's something you can understand in the context of Newtonian mechanics: http://en.wikipedia.org/wiki/Shell_theorem

Ok. As this spherical mass is collapsing, toward reaching its final state, wouldn't the strength of the gravitational field outside the mass be increasing? If so, how is that strength gradient communicated, since gravity waves wouldn't be emitted?

 

[bcrowell]

Ok. As this spherical mass is collapsing, toward reaching its final state, wouldn't the strength of the gravitational field outside the mass be increasing?

No. Have you looked at the WP article on the shell theorem?

 

[Ranku]

No. Have you looked at the WP article on the shell theorem?

Ya. The first principle says: A spherically symmetric body affects external objects gravitationally as though all of its mass were concentrated at a point at its center.

So the physical interpretation would be that the gravitational field outside the sphere would always be the same even if the sphere contracts because it does not depend on the radius of the sphere?
(By the way I am consulting the end notes in Alan Guth's The Inflationary Universe. )

The note also says: When the sphere has contracted to the new position, the final energy must be negative. I assume he is talking about gravitational potential energy, and negative means using a negative sign.

The note goes on to say: In most physical processes the exchange of gravitational energy is much smaller than the rest energy of the particles, but cosmologically the total gravitational energy can be very significant. Am not clear about this one.