Since LIGO has been able to detect the presence of gravitational waves, this implies that there is a density wave traveling through space with a high potential front and a low potential back side. Since gravity affects the amount of time that passes relative to an outside observer, do gravitational waves minutely slow/down speed up time when they travel across a region of space?

I'm also interested in learning if waves in the fabric of space time are strictly the same thing as the gravitational force being expressed as a wave. You can create a wave in a pond by throwing a rock, similar to black hole collisions. But, that doesn't necessarily mean gravity is itself a wave.

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    $\begingroup$ yes, they are perturbations to the spacetime metric, so they can cause length and time perturbations. $\endgroup$ – Bobak Hashemi Feb 24 '19 at 21:45
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    $\begingroup$ Gravity doesn't cause time dilation. It is time dilation that causes gravity. $\endgroup$ – safesphere Feb 25 '19 at 9:56

Gravitational waves are not density waves, any more than electromagnetic waves are density waves. Both propagate through a vacuum where there is no matter to have a density.

Gravitational waves are propagating wavelike metric perturbations in the Riemannian geometry of spacetime. The simplest ones, plane waves, are transverse. If they propagate in the $z$ direction, they affect spacetime intervals in the $x$ and $y$ directions (they squeeze $x$ while stretching $y$, then vice versa, then repeat), but they do not affect spacetime intervals in the $z$ and $t$ directions. So they don’t cause time dilation. Even if they did, the weak plane waves LIGO detects from far-distant sources perturb the metric of spacetime only at the level of one part in a billion trillion.

On the other hand, when two black holes or neutron stars merge, the intense gravitational waves close to the merging objects are strong and non-planar, and presumably perturb all components of the metric. I am reasonably sure that they do cause time to slow down and speed up in an oscillatory way for nearby observers.

A gravitational wave is not what creates gravity or how gravity is expressed. Gravity is created by the density and flow of energy and momentum and expressed as spacetime curvature. You can have static curvature without any kind of wave in it. For example, the Sun’s gravity is essentially static curvature. Gravitational waves are just ripples on top of the overall curvature. When the Sun has a solar flare, it creates a small gravitational wave on top of the vastly stronger curvature caused by a static Sun.

Some physicists hate the “trampoline” visualization of gravity-as-curvature, but at least it makes clear that gravity doesn’t require waves to affect how objects move through space. When you place a bowling ball (the Sun) on the trampoline, and then let a Ping-Pong ball (the Earth) roll around it, it’s not going around because the bowling ball is making waves on the trampoline. It is going around simply because the bowling ball has curved the trampoline.

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