5 ms·

Yes, gravitational wave are governed by the wave equation. A standard way to treat them is as a small perturbation around a known spacetime geometry. Then the m

by joe__f 5y ago

Yes, gravitational wave are governed by the wave equation. A standard way to treat them is as a small perturbation around a known spacetime geometry. Then the metric would be $g = g_0 + \epsilon h$, where $g_0$ is the background, $\epsilon$ is a small parameter and $h$ is the perturbation. In general Einstein's field equations govern the dynamics of $g$, and if you take the first order behaviour in $\epsilon$ around $g_0$ as flat space, then you recover the wave equation for $h$ as in the article you linked, with propagation speed $c$ the speed of light. (There are some additional subtleties about choice of gauge, but this is not physical). I'm not sure what you mean with your moon example.

CoastalCoder 5y ago
Thanks! I'm not ready to understand your explanation, but I can clarify the moon example at least. Suppose the gravitational attraction between the earth and moon is 2e20 Newtons. Now imagine something forces that attraction to strengthen from 2e20N to 3e20N. E.g. the Earth and moon get closer to each other, or the moon gets more massive somehow. When we talk about "detecting gravity waves", I understand that to mean that on Earth we've managed to detect that increase from 2e20N to 3e20N. My point was: perhaps that looks like the rising edge of a wave phenomenon, but it's not actually cyclic like I expect from a traditional "wave". So I couldn't understand why it's called a gravity wave.
- Beldin 5y ago
  Nitpick: gravity waves != gravitational waves. Unfortunately, I don't know enough to explain the difference.
  - cobaltoxide 5y ago
    "Gravity waves" are ordinary water waves, or other waves of a fluid, where gravity provides the restoring force: https://en.wikipedia.org/wiki/Gravity_wave https://en.wikipedia.org/wiki/Gravity_wave They have absolutely nothing to do with gravitational waves. Nonetheless, in the gravitational wave community (i.e. LIGO) we don't usually ever talk about true "gravity waves" so we use the terms interchangably. The exception is that "gravity waves" in the Earth and the atmosphere can couple to LIGO through ordinary Newtonian gravity, which is something we have to think about and exclude.
- cobaltoxide 5y ago
  Gravitational waves do not behave in the way you have described. > I understand that to mean that on Earth we've managed to detect that increase from 2e20N to 3e20N. This not what how gravitational waves behave. This assumption is not correct and will confuse you.
- xelxebar 5y ago
  If you're already comfortable with the Wave Equation, then it's somewhat straightforward. You start with some spacetime geometry (i.e. some "known metric") and then study small perturbations that obey the wave equation. The key is finding distributions of matter that, by Einstein's Equation, cause such perturbations to arise. In differential geometry, the device called a "metric" let's you define things like angles and distances on some space. This is generally denoted as g with the Greek letters mu and nu as subcripts. Just to give you a feel of what's going on, I'll leave out the subscripts, but what OP's saying is that g = k + h which says that g, the space-time metric, decomposes into some known, usually easy to work with metric k, plus some perturbations on top, h. In the math you put restrictions on h to make precise the "small perturbations" part. Anyway, what Gravity Waves boil down to are situations (read distributions of matter) that cause h to obey the wave equation. In other words, gravitational waves are spacetimes that have a component that waves "on top" of a given reference "background" spacetime. Of course, you could cherry pick your background such that anything looks like waves on top, but typically we choose the background to be Minkowskian (i.e. flat). FWIW, the above perturbative approach is called Linearized Gravity and is kind of a (nice) hack to restrict study of the really hairy non-linear Einstein Equation to cases that are manageable.

by joe__f 5y ago

CoastalCoder 5y ago

Thanks! I'm not ready to understand your explanation, but I can clarify the moon example at least. Suppose the gravitational attraction between the earth and moon is 2e20 Newtons. Now imagine something forces that attraction to strengthen from 2e20N to 3e20N. E.g. the Earth and moon get closer to each other, or the moon gets more massive somehow. When we talk about "detecting gravity waves", I understand that to mean that on Earth we've managed to detect that increase from 2e20N to 3e20N. My point was: perhaps that looks like the rising edge of a wave phenomenon, but it's not actually cyclic like I expect from a traditional "wave". So I couldn't understand why it's called a gravity wave.

Beldin 5y ago
Nitpick: gravity waves != gravitational waves. Unfortunately, I don't know enough to explain the difference.
- cobaltoxide 5y ago
  "Gravity waves" are ordinary water waves, or other waves of a fluid, where gravity provides the restoring force: https://en.wikipedia.org/wiki/Gravity_wave https://en.wikipedia.org/wiki/Gravity_wave They have absolutely nothing to do with gravitational waves. Nonetheless, in the gravitational wave community (i.e. LIGO) we don't usually ever talk about true "gravity waves" so we use the terms interchangably. The exception is that "gravity waves" in the Earth and the atmosphere can couple to LIGO through ordinary Newtonian gravity, which is something we have to think about and exclude.
cobaltoxide 5y ago
Gravitational waves do not behave in the way you have described. > I understand that to mean that on Earth we've managed to detect that increase from 2e20N to 3e20N. This not what how gravitational waves behave. This assumption is not correct and will confuse you.
xelxebar 5y ago
If you're already comfortable with the Wave Equation, then it's somewhat straightforward. You start with some spacetime geometry (i.e. some "known metric") and then study small perturbations that obey the wave equation. The key is finding distributions of matter that, by Einstein's Equation, cause such perturbations to arise. In differential geometry, the device called a "metric" let's you define things like angles and distances on some space. This is generally denoted as g with the Greek letters mu and nu as subcripts. Just to give you a feel of what's going on, I'll leave out the subscripts, but what OP's saying is that g = k + h which says that g, the space-time metric, decomposes into some known, usually easy to work with metric k, plus some perturbations on top, h. In the math you put restrictions on h to make precise the "small perturbations" part. Anyway, what Gravity Waves boil down to are situations (read distributions of matter) that cause h to obey the wave equation. In other words, gravitational waves are spacetimes that have a component that waves "on top" of a given reference "background" spacetime. Of course, you could cherry pick your background such that anything looks like waves on top, but typically we choose the background to be Minkowskian (i.e. flat). FWIW, the above perturbative approach is called Linearized Gravity and is kind of a (nice) hack to restrict study of the really hairy non-linear Einstein Equation to cases that are manageable.