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Regards,

Nenad

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- Thread starter Nenad
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Regards,

Nenad

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In regards to the question, the only events powerful enough to generate large enough distortions in the spacetime fabric are such events as supernovas, neutron stars colliding, etc.

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I didn't mean to cast doubt on whether they exist or not, but as you yourself say, physicists are only "fairly confident" of their existence. The reason they think they exist is because all theoretical models currently predict them, and there's no reason to think such models need to be altered, so, yes, there is a lot of confidence of their existence. But we can't know for sure whether they exist or not until we do detect them, and up until now we have not.Vast said:I think you’ll find that physicists are fairly confident that gravitational radiation exists.

We've been detecting electromagnetic radiation ever since the first creature evolved eyes, and it took us until Edison to manufacture it; well, ok, that's not true, we've known how to make fires for quite a while, but we had eyes way before that, so you get my point. It's kind of hard to create something you can't detect. The problem is gravity is extremely weak compared to electromagnetism (and, well, anything), so it's taken us this long to build detectors that theory predicts will be good enough to detect strong sources of gravitational radiation.Nenad said:

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Phobos

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εllipse said:there is a lot of confidence of their existence.

At least we can say they're confident enough to have spent a ton of money on trying to detect them!

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Regards,

Nenad

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Let's see, thats on pg 979, and the figures are:

you have a 500 ton steel beam 1 meter in radius, 20 m long, spinning as fast as it can before it flies apart (28 radians/second).

The power it emits in gravitational radiation is then 10^-23 ergs/second.

Basically, it's hopeless. Note that you need a quadropole mass moment, so a spinning sphere or near sphere like the Earth won't emit gravity waves, you need to spin something that's non-spherical.

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εllipse said:I didn't mean to cast doubt on whether they exist or not, but as you yourself say, physicists are only "fairly confident" of their existence. The reason they think they exist is because all theoretical models currently predict them, and there's no reason to think such models need to be altered, so, yes, there is a lot of confidence of their existence. But we can't know for sure whether they exist or not until we do detect them, and up until now we have not.

Let's not forget the indirect evidence from Binary Pulsar PSR 1913+16:

http://astrosun2.astro.cornell.edu/academics/courses//astro201/psr1913.htm

http://nobelprize.org/physics/laureates/1993/illpres/discovery.html

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Nenad said:.... The article stated that the US government already had technology consisiting of 3 cylindrical stuctures that can do so. The article also says that the technology....was obtained from a crashed alien spacecraft. ...

Yea, they're thinking about selling it to some Canadians in the Ontario province for an undisclosed obscene price; he,he.

However, if you're thinking about building your own gravity wave generator here's the approximation formula for determining the power (dE/dt) emitted from a rotating quadrupolar source:

[tex]P = \frac{8GI^2\omega^6}{5c^5}[/tex]

where [itex]\omega[/itex] is the angular frequency;

I is the moment of inertia (equal to [itex]2mr^2[/itex] for example for a spinning dumbbell arrangement); and the others are the usual constants.

This will give you some idea of the magnitude of the GW energy you can expect from any feasible arrangement.

Good Luck.

Creator

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Thanks for the input.

Regards,

Nenad

Regards,

Nenad

- #12

haushofer

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But, how does one derives a wave equation if you're stuck with a strong grav.field, and perturbation isn't any help?

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haushofer said:

But, how does one derives a wave equation if you're stuck with a strong grav.field, and perturbation isn't any help?

You can show that gravity is a well-posed initial value problem, which basically does what you want.

This is discussed in chapter 10 of Wald's "General relativity", which is about the "intial value" formulation of general relativity. The details are very involved, but basically it cobnsists of aqsking what sort of differential equations arise from Einstein's equations. It turns out that while they have an enormous number of terms, they are linear in the highest order derivative ("quasilinear") - this makes them _locally_ have many of the properties of linear equations of the same form. This includes the property of not having solutions propagating faster than 'c' when you look at the time evolution of the state of the system. You can do this by comparing two nearby (in time) 'states', hence only need 'local' results. (Definining the state of the system and separating out time and defining a global notion of time is a big part of the problem!). I haven't really looked at the details very closely, one may need one or more of the weak or strong energy conditions too. But if you want to read about it, Wald cover's the topic.

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But, how does one derives a wave equation if you're stuck with a strong grav.field, and perturbation isn't any help?

Well first of all linearized perturbation was only the textbook treatment. A perturbative method that is more robust exists, it is called the post-Newtonian expansion and it still assumes weak gravity but it uses the nonlinear terms in Einstein's equations. It's useful enough for modeling the types of inspiral signals that LIGO can detect.

But when that fails there are other analytic methods that you can use before turning to numerical relativity. Some people assume a nearly Kerr metric and expand in powers of the mass ratio. That is usually referred to as black hole perturbation theory. This is extremely effective for modeling extreme mass ratio inspirals, which are events you might expect to detect in LISA.

Also there is a perturbative way to model the near zone gravitational waves in a completely different way that works very well in the strong field. The catch is that the expression doesn't yield you the metric directly, it yields you the Zerelli function which, however, can be used to directly measure the strain on an interferometer (which is actually a more useful measure when you think about it).

Those are the analytic methods that I know of to calculate gravitational waves from compact binary inspiral. There is still an important need to model this more accurately than the analytic approximate methods can yield, which is why there is a whole field dedicated to this known as Numerical Relativity. People in that field try to evolve the binary orbits using the full non-linear Einstein equations. It is a highly challenging field that has seen many great breakthroughs in the past few years.

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