The sun's gravitational pull on the earth

[pervect]

I don't know if I agree with this. I can think of some really ridiculous ways for the sun to disappear that are HORRIBLY unlikely but not ruled out by relativity. For instance, what if the mouth of a wormhole suddenly opened up and sucked the Sun to the different part of the universe, and then the wormhole instantly evaporated? What if we measure the Sun where it is today, and then, by the uncertainty principle, the next time we measure it it has moved 10 light years away (the odds are incredibly tiny, but still, non-zero). I don't think that GR specifically prohibits these scenarios...and I'm sure there are others that would facilitate the Sun's sudden disappearance.

If you imagined a sphere in 3d space enclosing the sun and the wormhole, the total mass enclosed by the sphere would be the same before and after the sun passed through the wormhole.

I see that you've added the idea that the wormhole "instantly evaporates". This is no more possible than the sun "instantly evaporating".

As far as the wormhole part of the physics goes, here are a few popular references:

http://www.npl.washington.edu/AV/altvw69.html

If a positive electric charge Q passes through a wormhole mouth, the electric lines of force radiating away from the charge must thread through the aperture of the wormhole. The net result is that the entrance wormhole mouth has lines of force radiating away from it, and the exit wormhole mouth has lines of force radiating toward it. In effect, the entrance mouth has now been given a positive electric charge Q, and the exit mouth acquires a corresponding negative charge -Q. Similarly, if a mass M passes through a wormhole mouth, the entrance mouth has its mass increased by M, and the exit mouth has its mass reduced by an amount -M.

Another source:

http://golem.ph.utexas.edu/string/archives/000550.html

An interesting fact about wormholes is that they change in mass as an
object passes through them. To see this, imagine a wormhole connecting
two distinct asymptotically flat spacetimes. In each spacetime, the ADM
mass is conserved. Thus, if we pass an object of mass m through the
wormhole, from A to B, the ADM mass on either side
cannot change. This means that the mass of the mouth A
increases by m and the mass of mouth B decreases by m. In
other words, the wormhole has measured the mass of the object. Note
that this argument applies in any dimension in which the ADM mass makes
sense.

Note that you can read the original Suskind paper and Suskind's own rebuttal to his paper at http://arxiv.org/abs/gr-qc/0504039 http://arxiv.org/abs/gr-qc/0503097. This paper is not directly concerned with the topic, however, though it mentions the particular point I wanted to make, that when a mass passes through a wormhole, the entrance mouth gains the appropriate amount of mass, to satisfy the conservation laws.

The differential conservation law that prevents the sun from disappearing is \nabla_a T^{ab} = 0. This is the differential form of the conservation of energy and momentum. Essentially, you can move the sun around, but you just can't make it vanish.

More formally, as the second reference metions, the point is that the ADM mass (assuming an asymptotically flat background space-time, i.e. an isolated system) is conserved. This is analogous to the way that charge is conserved in classical E&M.

Just because you can imagine things happening doesn't make them physically possible. The proof of the impossibility is in the details of the conservation laws. Conservation of energy in GR is a bit trickier than the conservation of charge in E&M, but it's still not possible to make the sun instantly disappear.

 

[Quaoar]

What if we position a wormhole next to the Sun, feed in another Sun-sized star into the other end, thus forcing the exit of the wormhole to acquire mass -M. Wouldn't we have a net total mass of 0 at the Sun's position?

 

[DaveC426913]

Pretty sure the sudden absence of the Sun would NOT cause catastrophic rebound from the disappearance of the tidal forces. Quoth http://en.wikipedia.org/wiki/Tidal_acceleration" :

Earth's net equilibrium tide has an amplitude of only 3.23 cm, which is totally swamped by oceanic tides that can exceed one metre.

...for the moon. If you do the math, the Sun's tidal forces are about half as strong. So basically, the sudden disappearance of the Sun would result in an elevation drop of no more than 1.6cm, which would also not be instantaneous due to the Earth's elasticity. In addition, the difference between local elevation changes would be tiny (Probably on the order of nanometers for two sides of an Earthquake fault).

Well, it's not comparable to any old earthquake. It's the entire world.

Tornados can do a real number on a house, not so much because the winds are so high, but because they act across the entire surface of the walls at once and on the entire house at once.

Likewise, an earthquake acting locally will be dampened by all the ground around it abosorbing the motion, but one that that acts on every part of the Earth will be orders of magnitude larger.

 

[pervect]

What if we position a wormhole next to the Sun, feed in another Sun-sized star into the other end, thus forcing the exit of the wormhole to acquire mass -M. Wouldn't we have a net total mass of 0 at the Sun's position?

If we assume the wormhole was initially in a state where its exit mass was negligible compared to the sun, after the object of mass M passed through the wormhole you'd have the wormhole exit, with a mass of -M, the object that just passed through the wormhole, with a mass of +M, and the sun, with a mass M. Total mass = M.

This is the same as the mass near the exit of the wormhole before the object passed through (the inital exit mass of the wormhole, assumed to be negligible, plus the mass of the sun). If you assume that the mass of the exit of the wormhole is non-negligible, nothing much changes, except that the initial and final masses of the wormhole + sun are m_exit + m_sun. +M gets added to this because of the object passing through, and -M gets added to this because of the change in the exit mass of the wormhole.

You do need to assume asymptotic flatness to define the ADM mass in the first place (or an alternative would be to assume a static metric and replace the ADM mass with the Komar mass). Other than that there isn't much difference between the "disappearing charge" scenario and the "disappearing mass" scenario - neither one can actually happen. This becomes clearer when one tries to actually solve the problem rigorously by writing down the 4-potential for the E&M case, or the metric coefficients for the GR case.

 

[Danger]

Damn! A post that I entered about a page back seems to have disappeared, and now I can't remember what it was.

 

[Quaoar]

Ah, thanks for clearing that up pervect. Well, here's a method that will make the Sun's gravity disappear: Detonate a gigantic bomb at the center of the Sun so that the vast majority of its mass is ejected isotropically at nearly c. That way, in 8 minutes, all of the Sun's mass will fly past the Earth's orbit, leaving nothing for the Earth to orbit around (thanks to Gauss' law). Voila! :)

 

[Danger]

That way, in 8 minutes, all of the Sun's mass will fly past the Earth's orbit, leaving nothing for the Earth to orbit around

Of course, that would also leave no Earth.

 

[ZapperZ]

This thread has degenerated into "pointless speculation". Thus, all of you should know what happens to such threads.

Zz.

 

[pervect]

"Blowing up the sun" is a much more sensible thought experiment than making the sun disappear. It's totally impractical, of course, but it doesn't involve violating physical law. If the explosion is spherically symmetric, there will not be any significant gravity waves emitted when blowing up the sun because of Birkhoff's theorem, see for example http://en.wikipedia.org/wiki/Birkhoff's_theorem_(relativity) . The wiki article talks about pulsating stars, but the same argument applies to spherically symmetric explosions as it does to spherically symmetric pulsations - they don't emit gravitational radiation. The only reason there would be any gravity waves at all is because the sun has some angular momentum.

Hence, the first change in gravity in this thought experiment would occur when the debris physically passes the Earth. One can use spherical symmetry, Newtonian theory, and Gauss's law to get an approximately correct answer in this case (because of the aforementioned lack of gravity waves). The total gravitational force towards the point where the sun used to be will be proportional to the amount of mass remaining within a sphere of the radius of the Earth's orbit (assuming for simplicity that the Earth's orbit is essentially circular).

 

[Quaoar]

This thread has degenerated into "pointless speculation". Thus, all of you should know what happens to such threads.

Zz.

Not sure I agree it has degenerated to "pointless speculation." Pervect was explaining why having the mass disappear was unphysical...I don't see what's wrong with him setting the record straight.

 

[rbj]

"Blowing up the sun" is a much more sensible thought experiment than making the sun disappear. It's totally impractical, of course, but it doesn't involve violating physical law. If the explosion is spherically symmetric, there will not be any significant gravity waves emitted when blowing up the sun because of Birkhoff's theorem, see for example http://en.wikipedia.org/wiki/Birkhoff's_theorem_(relativity) .
...
Hence, the first change in gravity in this thought experiment would occur when the debris physically passes the Earth. One can use spherical symmetry, Newtonian theory, and Gauss's law to get an approximately correct answer in this case (because of the aforementioned lack of gravity waves).

not knowing GR well enough to do mathematics in it, that makes perfect sense. but what about an explosion (of energy comparable to novae) that spews at nearly c nearly all of the sun's matter out of the top and bottom along the axis of the orbital plane? that should send out a gravitational wave. does it beat the electromagnetic wave?

 

[pervect]

In GR, gravity waves travel at 'c' in a vacuum, just like light. Of course the interstellar media isn't quite a perfect vacuum. More on this later.

You will generate gravity waves when you have systems that are not spherically symmetric. An axis-symmetric explosion like the one you describe would indeed cause gravity waves to be emitted. It's not clear to me how to generte such a non-symmetric explosion. One way of generating gravity waves would be to implode the sun into a black hole, rather than exploding it. I'd suggest using the same x-ray implosion techniques that we use in H-bombs on a much larger scale. (I haven't really worked out the details.) The rotation of the sun would make the resulting implosion spherically assymetrical (it would only be axis symmetric) so that it would generate gravity waves.

Exploding the rotating sun in this way doesn't provide much in the way of gravity waves, as I mentioned. It turns out emitted power (luminosity) for rotating systems scales something like (M/2r)^5 in geometric units. Because M/2r is about 200,000 for the sun, we would be talking about a 10^25 or more increase in gravity wave production with the implosion technique - or alterantively, a 10^25 reduction factor if we just explode the sun.

People haven't seriously studied the idea of imploding the sun, of course, but they have started to study the expected gravity wave signatures from supernovae due to rotating core collapse (see for instance http://www.ligo.caltech.edu/docs/G/G020075-00.pdf ).

Offhand, I would expect that the interstellar medium would slow light down slightly, while not affecting the propagation speed of gravity nearly as much - because gravity interacts much more weakly with matter than electromagnetism does. So for a distant enough supernova, I'd expect that the gravity waves would arrive first, probably about the same time as the neutrino pulse, and the light would arrive later. The gravity waves and the neutrinos would essentially travel at c, the light would be slightly slowed down by its interaction with the interstellar medium.

We've already seen this effect when we happened to catch a neutrino pulse and the optical pulse from the same supernova. This took a little bit of luck. Of course, we haven't seen any gravity waves from Ligo yet, so we don't have any similar data on their timing.

If we do detect supernova with Ligo or Lisa, and detect the same supernova optically, we will probably be able to get some experimental data on the speed of gravity. Until then, I don't think we'll have much in the way of observational evidence. I think it was mentioned earlier in this thread that some experiments have been done, but on review it seemed questionable as to what the experiments had actually measured. A measurement of a gravity wave pulse and an optical pulse from a cosmic catastrophe would be much more direct.

 

[MeJennifer]

So does a rotating star generate gravity waves?

 

[Garth]

So does a rotating star generate gravity waves?

No, symmetric models do not produce gravitational waves, antipodal mass contributions cancel each other out.

Garth

 

[MeJennifer]

No, symmetric models do not produce gravitational waves, antipodal mass contributions cancel each other out.

Garth

Wait so an exploding rotational ball would not generate gravitational waves while a collapsing rotational ball would?
How come there is no symmetry between those situations? what is different?

It must be me not understanding all this but it is confusing to say the least:

Blowing up the sun" is a much more sensible thought experiment than making the sun disappear. It's totally impractical, of course, but it doesn't involve violating physical law. If the explosion is spherically symmetric, there will not be any significant gravity waves emitted when blowing up the sun because of Birkhoff's theorem, see for example http://en.wikipedia.org/wiki/Birkhoff's_theorem_(relativity) .

So here I am led to believe that an exploding rotating ball does not generate gravitational waves.

One way of generating gravity waves would be to implode the sun into a black hole, rather than exploding it. I'd suggest using the same x-ray implosion techniques that we use in H-bombs on a much larger scale. (I haven't really worked out the details.) The rotation of the sun would make the resulting implosion spherically assymetrical (it would only be axis symmetric) so that it would generate gravity waves.

But apparently a rotating ball that is imploding does generate gravitational waves because it is rotating.

Exploding the rotating sun in this way doesn't provide much in the way of gravity waves, as I mentioned. It turns out emitted power (luminosity) for rotating systems scales something like (M/2r)^5 in geometric units. Because M/2r is about 200,000 for the sun, we would be talking about a 10^25 or more increase in gravity wave production with the implosion technique - or alterantively, a 10^25 reduction factor if we just explode the sun.

Now I am led to believe that a rotating ball does generate gravity waves but is just not much.

So how about getting this in the form of a simple schema folks so that all those people who lack understanding, people like me, can get this right.

And let's agree on that does not generate any gravitational waves means not even if the amount is very very tiny.

So we have:

1. A rotating ball
2. A rotating exploding ball
3. A rotating collapsing ball

For any of those three situations do we have gravitational waves?

Furthermore does a rotating ball have a spherical shape in GR?
Furthermore what is the relationship (if any) between gravitational waves in rotating scenarios and the, sometimes called gravitomagnetic, Lense-Thirring effect and "geodetic" precession?

 

[LURCH]

A symetrical rotating star does not generate gravity waves. A symmetrical rotating star that is exploding is a very different scenario; one that most certainly does generate gravity waves.

 

[MeJennifer]

A symetrical rotating star does not generate gravity waves. A symmetrical rotating star that is exploding is a very different scenario; one that most certainly does generate gravity waves.

So, a rotating black hole does not generate gravitational waves either?

But is a rotating star symmetrical in GR?
In other words does GR predict rotating balls to be symmetrical, e.g. no bulge on the equator?

For instance neutron stars generate gravitational waves and they rotate.

 

[LURCH]

I've never heard that rotating eutron stars generate gravity waves. It is predicted that two neutron stars (or two black holes) orbitting very close to each other would produce them, I've not heard of any prediction that a single star rotating on its own axis could.

GR does predict that a rotating sphere will bulge at the middle, but this does not make it asymmetrical. It is symmetrical if you use the axis of rotation as the plane of reflection.

The idea behind gravitational waves is that they require some location within space to undergo a drastic change in gravitational field. The gravitational field around our Sun for example, is fairly homogenous no matter where one measures it. If you drew lines of longitude on the surface of the Sun, you would see them complete one revolution about every 25 days. But the force of gravity is nearly identical over all the lines of longitude, so the gravitational field is not fluctuating. Therefore, the Sun is not expected to generate any measurable gravitational waves.

 

[MeJennifer]

GR does predict that a rotating sphere will bulge at the middle, but this does not make it asymmetrical. It is symmetrical if you use the axis of rotation as the plane of reflection.

So then a rotating ball with an equatorial bulge is considered spherical symmetric?

 

[selfAdjoint]

So then a rotating ball with an equatorial bulge is considered spherical symmetric?

Not spherical. It has axial or cylindrical symmetry. That's appropriate, since it's rotating.

 

[MeJennifer]

Not spherical. It has axial or cylindrical symmetry. That's appropriate, since it's rotating.

Ok, so then how can people use Birkhoff's theorem as an argument against gravitational waves for rotating balls?
Isn't his theorem pertaining to spherical symmetry?

 

[Labguy]

Ok, so then how can people use Birkhoff's theorem as an argument against gravitational waves for rotating balls?
Isn't his theorem pertaining to spherical symmetry?

Yes, spherical symmetry, BUT, of the gravitational field at a distance. It is not about the shape (spherical or oblate) of the object itself.

 

[MeJennifer]

Yes, spherical symmetry, BUT, of the gravitational field at a distance. It is not about the shape (spherical or oblate) of the object itself.

What do you mean by "at a distance"?
Anything asymmetrical within the ball would cause gravitational waves would it not?

 

[Labguy]

What do you mean by "at a distance"?
Anything asymmetrical within the ball would cause gravitational waves would it not?

Pick a distance, any distance from a ball, rotating or not.

If within the ball (sphere) the net gravity is zero, beyond the ball it would be the Schwartzchild coordinates. That gives the "spherical symmetry" of the gravitational field. Only some cataclysmic event, as explained by many other posts above, would create the gravity waves. Don't know how else to explain it without having you go read a book.

 

[MeJennifer]

If within the ball (sphere) the net gravity is zero...

I am not sure what you mean by "net gravity is zero" within the ball since there is obviously resistance from EM forces to the gravitational collapase.

But anyway is that the case for a rotating ball with an equatorial bulge, that, as you call it, the net gravity is zero?

 

[SpaceTiger]

Gravitational radiation requires a time-varying quadrupole moment. A spinning object, even if bulged in the middle, would have a constant quadrupole moment. However, if it were also precessing, this would not be the case and it would emit gravitational radiation.