# Structure of a gravitational wave?

• ClamShell
In summary, the conversation discusses the concept of electromagnetic (EM) waves and their propagation in space due to the relationship between the electric and magnetic fields. The question is raised if gravitational waves (GW) have a similar relationship and what the orthogonal components would be. However, the analogy between EM and GW is not as close as initially thought, as the Einstein field equations of GR do not have the same structure as Maxwell's equations. It is noted that while there is something similar to the "push-pull" relationship in GR, there are not two different fields that are orthogonal to each other in the case of GW.
ClamShell
Questions concerning GW's are very common on PF,
but I think I have a new question on the concept.

Maxwell explains that EM waves(photons) propagate
in space due to a relationship between the sinusoidal
representations of the electric and magnetic fields
of the wave. Namely that these two sinusoids are
orthogonal and 90 degrees out of phase (if memory
serves). Kind of a push-pull relationship. IE, if these
components are not present there is no propagation
of the EM wave into space.

My question is that if EM waves are analogous to
to Gravitational Waves, what would be the orthogonal
components that would force the GW's to radiate
according to Maxwell's explanation of EM waves?

Without orthogonal components would not the GW
be stationary?

You may like to read about http://arxiv.org/abs/0908.1326" - in section 2 it is explained how for weak fields gravity can be treated, in some respect, in a similar way as electromagnetism.

Last edited by a moderator:
ClamShell said:
Namely that these two sinusoids are
orthogonal and 90 degrees out of phase (if memory
serves).
They're in phase.

ClamShell said:
My question is that if EM waves are analogous to
to Gravitational Waves, what would be the orthogonal
components that would force the GW's to radiate
according to Maxwell's explanation of EM waves?

Without orthogonal components would not the GW
be stationary?
The analogy isn't as close as you're thinking; in a gravitational wave there are not two different fields that are orthogonal to one another. The wave equation of GR is the Einstein field equations, which don't have the same structure as Maxwell's equations. There is something somewhat similar to the "push-pull" in GR, which is that contraction along one transverse axis requires expansion along the other transverse axis axis; this is because the Einstein field equations in vacuum are basically statements of conservation of the volume of a cloud of test particles.

One thing that is similar about the two is that in both cases, the vibrations are transverse. (In the case of gravitational waves, this is only strictly true in the far-field limit.) In the GR case, this is because a purely longitudinal plane wave propagating along the x-axis would be equivalent to a change of coordinates $x \rightarrow x'(x,t)$, which can't mean anything in GR because GR is completely invariant under any smooth change of coordinates.

One way to see that GR can't be strictly analogous to EM is that in the EM case you have two planes of polarization, like | and -, whereas in the GR case you have polarizations that look like + and x.

[EDIT] Arkajad makes a good point about the analogy in the weak-field case.

Last edited:
bcrowell said:
The analogy isn't as close as you're thinking; in a gravitational wave there are not two different fields that are orthogonal to one another. The wave equation of GR is the Einstein field equations, which don't have the same structure as Maxwell's equations. There is something somewhat similar to the "push-pull" in GR, which is that contraction along one transverse axis requires expansion along the other transverse axis axis; this is because the Einstein field equations in vacuum are basically statements of conservation of the volume of a cloud of test particles.

Thanks for pointing out that E & B are in phase for EM waves. What I had hoped,
was that for GW's the orthogonal fields would be gravity and momentum. Thanks
for the eye-opener.

## 1. What is a gravitational wave?

A gravitational wave is a ripple in the fabric of space-time that is caused by the acceleration of massive objects, such as merging black holes or neutron stars. It was predicted by Albert Einstein's theory of general relativity and has been observed by various experiments and detectors.

## 2. How is a gravitational wave created?

A gravitational wave is created when there is a disturbance in the fabric of space-time. This can occur when massive objects, such as black holes or neutron stars, accelerate or merge with each other. As they move, they create ripples in space-time that travel outwards at the speed of light.

## 3. What is the structure of a gravitational wave?

A gravitational wave has a specific pattern of alternating stretches and compressions in space-time, similar to the waves on the surface of a pond. This pattern is known as a gravitational wave's strain and can be detected by specialized equipment, such as laser interferometers.

## 4. How is the structure of a gravitational wave measured?

The structure of a gravitational wave is measured using interferometry, which involves splitting a laser beam into two paths and then recombining them. When a gravitational wave passes through, it causes a change in the distance traveled by each beam, resulting in an interference pattern that can be measured and analyzed.

## 5. What can we learn from studying the structure of gravitational waves?

Studying the structure of gravitational waves can provide valuable insight into the universe and the objects that exist within it. By observing the properties of gravitational waves, we can learn more about the behavior and evolution of massive objects, as well as the nature of space and time. It can also help us validate and refine our understanding of Einstein's theory of general relativity.

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