# Why are Gravitational Waves Produced?

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1. Aug 4, 2015

### Mistake Not...

I know GWs are produced by moving masses, but I can't find an explanation as to why it happens.

A system would lose energy to gravitational radiation. Does the radiation get produced spontaneously, or would it be because the mass has to move through space-time which holds it back somewhat (this is the only reason I can think of that would make it lose energy)?

My question might be slightly confusing, but in essence: Why is gravitational radiation produced?

Thanks
Geoff

2. Aug 4, 2015

### Orodruin

Staff Emeritus
The physical answer to the question would be: "Because this is what happens when masses accelerate according to Einstein's field equations."

You may go further and ask "Why do Einstein's field equations look as they do?", but that is a philosophical question rather than a physical one.

Compare to the generation of electromagnetic radiation, it is produced based on the acceleration of charges and this is described by Maxwell's equations. There is no underlying "why", it is simply how Maxwell's equations work.

3. Aug 4, 2015

### ChrisVer

The Einstein equations tells you that the Einstein Tensor ($G_{\mu \nu}$) is proportional to the energy-momentum tensor $T_{\mu \nu}$:
$G_{\mu \nu} \equiv R_{\mu \nu} - \frac{1}{2} g_{\mu \nu} \mathcal{R} = \alpha T_{\mu \nu}$

If now you are in a large distance from a static matter distribution you will live in a metric $g_{\mu \nu}$
However if there are some changes in the matter distribution (that is in the $T_{\mu \nu}$) then your metric is also going to be changed to g':
$g_{\mu \nu}^\prime = g_{\mu \nu} + h_{\mu \nu}$
With h playing the role of a perturbation due to matter distribution changes.
Now if you input that metric g', in the Einstein equations (and making some assumptions like that h is small), you are going to reach the result that h sattisfies a wave equation.

4. Aug 4, 2015

### Orodruin

Staff Emeritus
It should be pointed out that this wave equation has a source term which will be dependent on the changes in the matter distribution, just as there will be a source term in the electromagnetic wave equation which depends on the changes in the charge distribution.

5. Aug 4, 2015

### A.T.

As Orodruin suggested, you should try to understand why accelerated charges produce EM waves. It's basically because changes in the EM-field propagate at a finite speed. There are many resources on this, for example:
http://www.tapir.caltech.edu/~teviet/Waves/empulse.html

Changes in gravitational fields also propagate at a finite speed, so you have a similar effect.

6. Aug 4, 2015

### bcrowell

Staff Emeritus
Gravitational waves are not just produced because a mass is moving. You need a mass that is accelerating (and the acceleration has to be at a varying rate).

Objects don't move through spacetime. Objects move through space.

It doesn't make sense to imagine a physical effect arising because an object is moving through space. Motion is relative, so a frame of reference always exists in which the object is at rest (at a given moment in time).

Your "why" question could be interpreted as asking (1) for a logical explanation of why such an effect must occur, or (2) for an underlying physical mechanism. As others have pointed out, we don't know of any answer to #2. Re #1, here's a simple argument. Special relativity says that information can't propagate at speeds greater than c. General relativity is a different deal, but roughly speaking we would expect the same restriction to apply. If I could wiggle the earth and *instantaneously* produce a gravitational effect on the moon, I'd be propagating information at a speed greater than c. Therefore there must be a time lag for gravitational effects to propagate, which must mean that the effects propagate as waves.

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