B Do Objects in Motion Create Gravitational Waves?

[Ross B]

does any object with mass that moves create a gravity wave? So if I wave my hand it is in fact creating gravity waves, just very small ones

 

[ISamson]

does any object with mass that moves create a gravity wave? So if I wave my hand it is in fact creating gravity waves, just very small ones

Yes.

 

[phinds]

does any object with mass that moves create a gravity wave? So if I wave my hand it is in fact creating gravity waves, just very small ones

I think "very small" VASTLY overstates the strength of that particular gravity wave

 

[ZapperZ]

I think "very small" VASTLY overstates the strength of that particular gravity wave

Maybe he/she is severely overweight.

Zz.

 

[phinds]

Maybe he/she is severely overweight.

Zz.

Yeah, but that would mean he/she would have to shake his/her belly rather that a hand wave.

 

[Vanadium 50]

does any object with mass that moves create a gravity wave?

Yes.

Huh? Where did you get that? An object that is moving at constant velocity does not create a gravitational wave.

 

[ISamson]

Huh? Where did you get that? An object that is moving at constant velocity does not create a gravitational wave.

Aren't we talking about a hand moving in space. Is that constant speed?

 

[Ross B]

Huh? Where did you get that? An object that is moving at constant velocity does not create a gravitational wave.

why does an object moving at constant velocity not not create a gravitational wave? like the wake from a boat

even if my hand was stationary the molecules/atoms within my hand are accelerating and decelerating so they would all be , individually, creating, gravity waves

if space is elastic, as a body moves thru space it deforms space and in its wake space must snap back to its original position, that deformation of space, assuming it is not a linear deformation, would cause space itself to accelerate/decelerate/strech/compact, all other factors remaining the same?

 

[Nugatory]

why does an object moving at constant velocity not not create a gravitational wave? like the wake from a boat.

Consider that when an object is moving at a constant velocity (relative to what?) then there is an inertial frame in which it is not moving at all... and all frames must agree about the presence or absence of gravitational waves, so if you can demonstrate that they aren't present using one frame, then you know they aren't present using any frame.

The boat is moving through the water, displacing it and creating waves in it. But that analogy doesn't work for gravitational waves because space is not a substance that you displace as you move through it.

if space is elastic, as a body moves thru space it deforms space and in its wake space must snap back to its original position, that deformation of space, assuming it is not a linear deformation, would cause space itself to accelerate/decelerate/strech/compact, all other factors remaining the same?

You may have been misled by pop-sci presentations that speak of spacetime as a "fabric", a thing that stretches and deforms and could have properties such as elasticity. It's not.

 

[Ross B]

The boat is moving through the water, displacing it and creating waves in it. But that analogy doesn't work for gravitational waves because space is not a substance that you displace as you move through it.

is "displace" just another way of saying "deform" which is another way of saying "changes some property of"? It is uncontroversial that a massive object changes the properties of (displaces) space around it as it move thru space

"You may have been misled by pop-sci presentations that speak of spacetime as a "fabric", a thing that stretches and deforms and could have properties such as elasticity. It's not."

space "deforms" around a massive objects, and therefore any object with mass. Implicit in that statement is space "un-deforms" after the object has passed by.

 

[Ibix]

space "deforms" around a massive objects, and therefore any object with mass. Implicit in that statement is space "un-deforms" after the object has passed by.

You have to remember that GR models spacetime, not space. Space is what you get when you slice 4d spacetime up into 3d sheets. So "space when you are near a massive body" and "space after the massive body has passed" are two completely separate parts of spacetime - nothing is actually deforming. Any sensible definition of "slicing up spacetime" will give you a sequence of spaces that change geometry smoothly, but the change is the change of slice you are calling "space, now", not from any deformation.

Some spacetimes include gravitational waves (not gravity waves - those are a kind of surface wave in fluids). Some do not. The spacetime around a body moving in a straight line can't because a distant inertial observer could see the body as stationary.

 

[Orodruin]

Pet peeve: It is important to separate the concept of gravity waves from that of gravitational waves. They are not the same thing.

 

[m4r35n357]

Pet peeve: It is important to separate the concept of gravity waves from that of gravitational waves. They are not the same thing.

Please everyone, it should not take until the 12th post to correct this.

 

[Orodruin]

Please everyone, it should not take until the 12th post to correct this.

To be fair, Ibix mentioned it in post #11 while I was typing and linking.

 

[m4r35n357]

To be fair, Ibix mentioned it in post #11 while I was typing and linking.

A couple of posters mentioned it in passing I know, but until your post nobody corrected it.

 

[Ross B]

so around a massive object, as the space component of spacetime does not deform, I assume only time deforms?

 

[Orodruin]

so around a massive object as the space component of spacetime does not deform, I assume only time deforms?

There is no such thing as "the space component". The separation into space-like slices is quite arbitrary and can be done in many different ways.

The pro-tip is that you will not be able to understand what is actually going on from extrapolating popularised descriptions or even more accurate descriptions that use English language. The reason is that language is not precise enough. The terms used do have a precise mathematical meaning, but that can be misrepresented with words having several similar meanings in English. The mental picture you are painting will likely not be accurate. Bottom line is: never use what you read in popular science to extrapolate arguments. Popular science is great for learning about science and creating interest in it, but it is rather useless for learning actual science.

 

[Ross B]

Im using Serway edition 4...am I wasting my time

Surely all I have to know is that a massive body moving thru space
the space ahead of the body has a number of parameters (one of those parameters is gravity?)
the massive body changes some of those parameters within its immediate surroundings
once the massive body has passed by, space returns to empty space

is that fundamentally flawed?

 

[Ibix]

so around a massive object, as the space component of spacetime does not deform, I assume only time deforms?

No. Nothing deforms. Spacetime is the shape it is. It doesn't change.

If our poor limited human intellects insist on slicing 4d spacetime into a sequence of 3d volumes, and calling each volume "space" and giving each one a sequence number we call "time", then each subsequent volume may be a different "shape". You could regard each one as deformed compared to its neighbour. But nothing is actually changing shape - you are simply looking at a sequence of slightly differently shaped slices of spacetime and mistaking that for one slice that changes shape. So there's no sense of "elastic deformation of a fabric".

 

[Nugatory]

Pet peeve: It is important to separate the concept of gravity waves from that of gravitational waves. They are not the same thing.

It's been fixed in the thread title.

 

[Ross B]

so if a massive object has absolutely no impact, of any kind what so ever, on any parameter of the space time around it - how does any other object know, at a distance, it is there?

 

[Ibix]

so if a massive object has absolutely no impact, of any kind what so ever, on any parameter of the space time around it - how does any other object know, at a distance, it is there?

Of course it has an effect. Those successive slices of spacetime are (or can be, anyway) different "shapes" for a reason. It's just that describing that effect as "distorting space" is hopelessly inadequate for getting any actual physics done.

For example, in the Schwarzschild spacetime there's an obvious way of slicing spacetime so that each slice ("all of space at this time") is identical. There is gravity there. But what's being distorted? Everything is the same, always has been and always will be. Sure, the geometry near the mass is different near the mass and far from the mass. But that's not because one of them changed shape to look like the other.

 

[Nugatory]

Im using Serway edition 4...am I wasting my time

Serway is a respectable enough textbook, but its few pages on general relativity are completely superficial: no differential geometry, no tensors, no coordinate transforms, no Einstein Field Equations. This may be because of their stated goal of introducing no math beyond first year calculus.

Carroll (https://www.preposterousuniverse.com/grnotes/) would be a good place to start in on GR; you can try the "no-nonsense overview" first if you don't want to take on the whole thing. The chapter on gravitational waves is at https://preposterousuniverse.com/wp-content/uploads/grnotes-six.pdf

 

[Imager]

Popular science is great for learning about science and creating interest in it, but it is rather useless for learning actual science.

This should be on T-Shirts!

 

[timmdeeg]

Of course it has an effect. Those successive slices of spacetime are (or can be, anyway) different "shapes" for a reason. It's just that describing that effect as "distorting space" is hopelessly inadequate for getting any actual physics done.

I think "distorting space" makes sense if interpreted as periodically stretching and squashing of space, as illustrated here by means of the ring of freely falling particles.

 

[Ibix]

I think "distorting space" makes sense if interpreted as periodically stretching and squashing of space, as illustrated here by means of the ring of freely falling particles.

That animation works by making a choice about what "space" means, slicing spacetime into a sequence of spatial slices, and then presenting that sequence of slices in an animation. That's fine. But it's presenting a sequence of distinct, slightly different things. In trying to understand GR it's a mistake to see it as one thing changing, because your initial choice of slicing spacetime into space was an arbitrary one.

 

[timmdeeg]

But it's presenting a sequence of distinct, slightly different things. In trying to understand GR it's a mistake to see it as one thing changing, because your initial choice of slicing spacetime into space was an arbitrary one.

Saying "one thing" do you mean the ring? To my understanding the source of the GW causes geodesic deviation which the "distortion" of the ring shows. Can you please elaborate a little more "because your initial choice of slicing spacetime into space was an arbitrary one." It seems I'm missing something important here.

 

[Ibix]

Can you please elaborate a little more "because your initial choice of slicing spacetime into space was an arbitrary one."

It's the block universe again. Take each frame (in the filmography, not physics sense) of the animation and print it. Stack up the printouts. Now dissolve the paper and leave the ink. This is the block universe and the wiggly columns of ink are the worldtubes of the dots.

To make the animation you need to put the paper back in. The paper is your choice of what "space" means. And in GR, as in SR, there's no reason to prefer horizontal or sloped pieces of paper. It's an arbitrary choice. Furthermore, the pieces of paper aren't expanding or contracting. Each one has a larger or smaller scale compared to its neighbour, but nothing is changing - unless you mistake the sequence of similar things for a single thing changing.

 

[Paul Colby]

So there's no sense of "elastic deformation of a fabric".

What about curvature? It's not zero in the neighborhood of a mass. I think I "get" that space-time doesn't "evolve" because time is included from the start and I also get vacuum is "nothing" part. I spent a lifetime viewing electromagnetic fields as dynamical why is this now verboten for curvature?

 

[PeterDonis]

I spent a lifetime viewing electromagnetic fields as dynamical why is this now verboten for curvature?

EM fields aren't dynamical either if you view them from the spacetime viewpoint. From the spacetime viewpoint, an EM field is an assignment of a 4-vector (the potential) to every event in spacetime, which has to satisfy certain equations (Maxwell's Equations in their spacetime form). Such an assignment isn't "dynamical" any more than spacetime itself is: it's a 4-dimensional object that just is, it doesn't "change".

If, OTOH, you want to view EM fields as dynamical, you have to pick some splitting of spacetime into "space" and "time", and then view the EM field as varying over "space" and evolving in "time". You can do the same thing with spacetime curvature: for example, you can view the spacetime curvature of a gravitational wave as a stretching/squeezing of "space" that changes with "time". The drawback of doing this is that there is no unique splitting of spacetime into "space" and "time", so any such choice of splitting will end up putting things into your model that are artifacts of that particular choice. (The same is true of the EM field: for example, which part of the field you call "electric" and which part you call "magnetic" is an artifact of your particular choice of how to split spacetime up into space and time.) But if you're willing to accept that drawback, the procedure itself is perfectly legitimate.

 

[timmdeeg]

To make the animation you need to put the paper back in. The paper is your choice of what "space" means. And in GR, as in SR, there's no reason to prefer horizontal or sloped pieces of paper. It's an arbitrary choice. Furthermore, the pieces of paper aren't expanding or contracting. Each one has a larger or smaller scale compared to its neighbour, but nothing is changing - unless you mistake the sequence of similar things for a single thing changing.

Yes. I just saw that also Wikipedia talks about distortion: " As a gravitational wave passes through the particles along a line perpendicular to the plane of the particles (i.e. following the observer's line of vision into the screen), the particles will follow the distortion in spacetime ". This misleads to believe that space is something physical which can be stretched ect. In deed, as in the case of the expanding universe one should think of changing distances instead.
I think the phrase "distortion of space" is ok as long as it isn't understood wrongly. The same is true talking about "curved spacetime".

 

[Paul Colby]

But if you're willing to accept that drawback, the procedure itself is perfectly legitimate.

Agreed, however, this from a space-time view nothing is dynamical seems like a vacuous viewpoint. Come rain or shine one still must solve a system of hyperbolic equations to understand the physics of an isolated or cosmological system. Other than dispelling layperson language misuse, this nothing is dynamical verbiage seems to offer little in the way of understanding, IMO.

 

[PeterDonis]

this from a space-time view nothing is dynamical seems like a vacuous viewpoint. Come rain or shine one still must solve a system of hyperbolic equations to understand the physics of an isolated or cosmological system

This is a matter of terminology, not physics. If you want to insist that any time you are solving hyperbolic differential equations, you are modeling a "dynamical" system, go ahead. As long as the precise meaning of your terminology is known, there's no problem in understanding your meaning, and "dynamical means hyperbolic differential equations" is precise. But not all physicists use that terminology, so when you see them saying that "spacetime is not dynamical", it's important to know that they mean something different by the word "dynamical" than you do--they certainly aren't claiming that the differential equations in question are not hyperbolic.

 

[Paul Colby]

it's important to know that they mean something different by the word "dynamical" than you do

Then it's certainly fair to ask what is this new meaning of the word "dynamical" of which space-time is not. I only ask because the way I was raised, space-time is governed by hyperbolic field equations as are all other fields. The subject was referred to as classical dynamics, electrodynamics, geometrodynamics ect. I must have missed a memo or something.

 

[PeterDonis]

it's certainly fair to ask what is this new meaning of the word "dynamical" of which space-time is not

I don't know that any of the scientists who use the word in the way I describe have provided a precise definition; but I think it is something along the lines of "dynamical" implying "changing with time", where "time" is some external parameter rather than an internal property of the model. Spacetime, as a model, does not have "time" as an external parameter, and does not describe a succession of "states" as a function of "time". It just describes a single 4-dimensional geometry.

One could certainly argue about which meaning is more appropriate for the word "dynamical", but as I said, that's a matter of terminology, not physics. The physics is, as you say, that the 4-dimensional spacetime geometry is obtained by solving a set of hyperbolic differential equations.

 

[PeterDonis]

The subject was referred to as classical dynamics, electrodynamics, geometrodynamics ect

The physicists who use the term "geometrodynamics" are not, as far as I can tell, the same ones who say that spacetime is not "dynamical". But neither are the physicists who use the term "geometrodynamics" all (or even a majority, as far as I can tell) of the physicists working in general relativity or some closely related field.

 

[Paul Colby]

The physicists who use the term "geometrodynamics" are not, as far as I can tell, the same ones who say that spacetime is not "dynamical". But neither are the physicists who use the term "geometrodynamics" all (or even a majority, as far as I can tell) of the physicists working in general relativity or some closely related field.

It's a term coined by Wheeler back in the day. There are whole sections of MTW that treat the local time evolution of 3-space so this is a concept which has technical meaning. I certainly could get behind there not being a globally defined universal time parameter but I would stop short of redefining the meaning of "dynamical" (which has been a part of physics for hundred of years) just so one could say that space-time isn't "dynamical". Sounds like a small group of researchers may have adopted this terminology but unless it has a precise meaning I see little benefit gained in adopting it.

 

[pervect]

There is no such thing as "the space component". The separation into space-like slices is quite arbitrary and can be done in many different ways.

It is rather ambiguous. I've got my own preference for how to make a split, via a mechanism that passes for "an observer". In simple terms for the OP, I'd describe this mechanism is just the set of worldlines of observers who are considered "at rest" and form an extended frame. (Some writers call this a frame, but sometimes other writers mean something else by a frame :( ). The technique works best in unchanging, i.e. static or stationary, space-times, where it's fairly obvious what these observers are, but in a pinch any set of observers will do, as long as they are agreed-upon. The wordline of this infinite set of observers forms a timelike congruence which fills space-time. Then using this congruence, one can use the Bel decomposition https://en.wikipedia.org/wiki/Bel_decomposition to decompose the RIemann (there's another technical term, which, for the benefit of the OP, I'll explain as representing the fundamental entity that describes the curvature of space-time). The Riemann decomposes , in the context of general relativity (GR), into three parts. (See wiki for when you might need four, but it's off-topic, it's not GR). One of these parts, calls the "topogravitic" part, can be interpreted as representing the purely spatial part of the curvature, as defined by the set of observers.

A basic issue I have though, is that while I think of things this way, it's unclear how many other people do - though it is in the literature, though not as prominently as it's explanatory power merits (in my opinion). So the techincal reader needs a lengthly explanation, and the non-technical reader has their own concepts, which may or may not be fundamentally compatible with GR, and which as a writer, we have no idea of what they are.. (Unfortrunately, it's rather likely that the non-technical readers concept of space and space-time is not even compatible with special relativity, which means automatically that it's not compatible with GR as GR is built on SR, special relativity. This makes writing about GR rather challenging.).

Anyway, with all this background out of the way, we can provide a answer to the original question, if one accepts the basic approach. Ideally we'd agree on the set of observers, but basically the electrogravitic part of the Riemann is equal to the topogravitic part in a vacuum. So with this definition, we'd say that there is a "space curvature" component of the GW. Otherwise we'd need both the electrogravitic and topogravitic parts to be zero, leaving the only source of curvature as the magnetogravitic part, and I don't believe that's possible.

One other thing I want to mention. I think that many people expect the set of observers regarded as being "at rest" to at least approximate a rigid body, as I think that's probably the most common approach to understanding space. This follows from the old, pre-relativistic idea of distance being measured with meter sticks, which are presumed to be rigid bodies. One will find a lot of explanations of GW's that basically do not take this approach, because it's mathematically more convenient not to. I feel that this causes a lot of conceptual mis-understandings and mis-communications, but it's unclear what to do about it. In a very common approach, observers "at rest" are considered to be those observers who follow geodesics, i.e. observers who have no proper acceleration. These observers do not maintain even approximately a constant separation :(.

I should mention that my second-favorite approach to the Bel decomposition for conceptual understanding is the usage of Fermi-normal coordinates, with the idea that these represent what happens if we choose coordinates which allow one to apply a lot of one's Newtonian intuitions. But the issue isn't fundamentally coordinate dependent, it can be talked about in non-coordinate (tensor) terms, which is why I prefer the Bel decomposition approach.

 

[PeterDonis]

It's a term coined by Wheeler back in the day. There are whole sections of MTW

Yes, I'm familiar with them and with the "superspace" formalism that Wheeler helped to develop. I'm just pointing out that that's not the only way to approach GR, and that other GR textbooks don't have the same emphasis on this particular aspect. (I don't remember Wald using the term "geometrodynamics" at all, for example.)

I certainly could get behind there not being a globally defined universal time parameter

It's more than that. It's that, although it is certainly possible to approach GR by viewing it as describing the "time evolution" of 3-geometries (as the superspace approach does), it is not necessary to do so. One can also take the viewpoint that a solution of the EFE describes a single 4-geometry. I personally think both viewpoints can be useful, and I don't think it's either useful or necessary to insist on adopting just one of them and not using the other at all.

I would stop short of redefining the meaning of "dynamical" (which has been a part of physics for hundred of years) just so one could say that space-time isn't "dynamical". Sounds like a small group of researchers may have adopted this terminology

I don't think it's a small group, at least not in the GR community. But I have not tried to come up with any actual numbers.

 

[PeterDonis]

redefining the meaning of "dynamical" (which has been a part of physics for hundred of years)

I'm also not sure this is true in the precise sense of "dynamical" you are using (i.e., that "dynamical" means "described by hyperbolic differential equations"). The term "dynamical" has been around for quite a while, but I'm not sure it has been understood as having that precise meaning for that same amount of time. But that's a question of history, not physics.

 

[laymanB]

Spacetime, as a model, does not have "time" as an external parameter, and does not describe a succession of "states" as a function of "time". It just describes a single 4-dimensional geometry.

This discussion is beginning to shed some light on my questions from the thread I started on infinite versus finite space. Very interesting and illuminating.

Does this spacetime model (viewing spacetime as a single 4-dimensional, non-evolving geometry) apply only to the universe as a whole, or can it be used for a subset of the whole universe (ie. the observable universe)?

 

[laymanB]

I don't claim to understand all of this but let me ask a couple questions.

If there are multiple solutions to the Einstein Field Equations that give you a model of spacetime that works for each, what is the justification for using the FRW metric as opposed to some other metric?

Is this idea of splitting up space and time into arbitrary components similar to the idea of no absolute reference frame in relativity? The mathematical models still account for the observational data and make accurate predictions by choosing an arbitrary way to slice spacetime, but you are left with artifacts that only correspond uniquely to your choice of how to slice it?

 

[PeterDonis]

Does this spacetime model (viewing spacetime as a single 4-dimensional, non-evolving geometry) apply only to the universe as a whole, or can it be used for a subset of the whole universe (ie. the observable universe)?

You can view any open region of spacetime (such as the observable universe) in the way I described.

 

[PeterDonis]

Is this idea of splitting up space and time into arbitrary components similar to the idea of no absolute reference frame in relativity?

It's the same idea.

The mathematical models still account for the observational data and make accurate predictions by choosing an arbitrary way to slice spacetime, but you are left with artifacts that only correspond uniquely to your choice of how to slice it?

In principle you don't have to choose an arbitrary way to slice spacetime in order to make predictions; you can formulate everything in terms of coordinate-independent quantities. In practice choosing coordinates (i.e., choosing an arbitrary way to slice up spacetime into space and time) often makes it much easier to make predictions, which is why it's so often done.

 

[pervect]

I don't claim to understand all of this but let me ask a couple questions.

If there are multiple solutions to the Einstein Field Equations that give you a model of spacetime that works for each, what is the justification for using the FRW metric as opposed to some other metric?

Is this idea of splitting up space and time into arbitrary components similar to the idea of no absolute reference frame in relativity? The mathematical models still account for the observational data and make accurate predictions by choosing an arbitrary way to slice spacetime, but you are left with artifacts that only correspond uniquely to your choice of how to slice it?

A lot depends on what you mean by "different solution". If you have some solution to EInstein's field equations, and you derive a new solution from the old solution by a mathematical transformation (in this case, the appropriate technical name for the appropriate transformation would be a diffeomorphism), do you regard the solution as "different"?

I suspect from your question that you do, but I regard the solutions as equivalent, and I'd describe changing the coordinates via a transformation to a new set of coordinates gives a different representation of the same solution, not a different solution.

To borrow an analogy, suppose you have a map of some section of land. And you rotate the map by some angle. Is it a "different map" after you rotate it, or is it "the same map, rotated"?

Some thought about what the "observations are" is helpful. On the map analogy, "observables" might be the length of trips (curves) that we draw on the map. Then the mathematical point is that rotating the map doesn't change the length of any curve, of any trip.

I say "borrow an analogy" because the original inspiration for this is a section called "The Parable of the Surveyor" from Taylor & Wheeler's "Space-time physics". Note that a "change in reference frame" in special relativity is called a Lorentz boost (it's also a diffeomorphism, like the others, a specific example that applies to SR), and it's mathematically quite similar to the mathematics that describe rotating a map, which is the original point of the analogy.

 

[laymanB]

A lot depends on what you mean by "different solution". If you have some solution to EInstein's field equations, and you derive a new solution from the old solution by a mathematical transformation (in this case, the appropriate technical name for the appropriate transformation would be a diffeomorphism), do you regard the solution as "different"?

I suspect from your question that you do, but I regard the solutions as equivalent, and I'd describe changing the coordinates via a transformation to a new set of coordinates gives a different representation of the same solution, not a different solution.

To borrow an analogy, suppose you have a map of some section of land. And you rotate the map by some angle. Is it a "different map" after you rotate it, or is it "the same map, rotated"?

Some thought about what the "observations are" is helpful. On the map analogy, "observables" might be the length of trips (curves) that we draw on the map. Then the mathematical point is that rotating the map doesn't change the length of any curve, of any trip.

I say "borrow an analogy" because the original inspiration for this is a section called "The Parable of the Surveyor" from Taylor & Wheeler's "Space-time physics". Note that a "change in reference frame" in special relativity is called a Lorentz boost (it's also a diffeomorphism, like the others, a specific example that applies to SR), and it's mathematically quite similar to the mathematics that describe rotating a map, which is the original point of the analogy.

Thanks, most of this is above my current knowledge but I think I understand what you are saying about derivations of prior equations not being "new" ones. And I think I can understand qualitatively about changing coordinate systems through transformations not altering invariant quantities.

Let me start with some more basic questions.

Are there solutions to the EFEs that are logically and mathematically consistent, yet no one uses them?

How do metrics like FRW correspond to the EFEs?

Thanks for your time.

 

[PeterDonis]

Are there solutions to the EFEs that are logically and mathematically consistent, yet no one uses them?

If by "uses them" you mean uses for practical modeling of something we expect to actually observe, sure: the Godel metric is the first example that comes to my mind. I'm sure there are many others that nobody has bothered to discover--after all, there are an infinite number of possible solutions, mathematically speaking.

How do metrics like FRW correspond to the EFEs?

They are solutions of them.

 

[Ibix]

How do metrics like FRW correspond to the EFEs?

Einstein's field equations relate the geometry of spacetime to the matter and energy distribution. You specify how the matter behaves and where it is at some point. You feed that into the EFEs and get sixteen simultaneous non-linear differential equations. If you've chosen a friendly setup many of those equations turn out to be 0=0 and you may be able to solve the rest. If not, you need a powerful computer.

Either way you end up with a metric tensor, which describes the geometry of spacetime given that distribution of matter. Schwarzschild started with a universe empty except for a spherically symmetric mass and derived the Schwarzschild metric, which works well for things like the solar system where 99%-ish of the mass is the Sun. Friedmann, Lemaitre, Robertson and Walker started with a universe completely filled with a same-everywhere mass distribution and came up with the FRW or FLRW metric, which works well on the scale where galaxies are dust grains.

There are a fair few known solutions, but an awful lot of interesting stuff (e.g. the binary mergers LIGO detects) can only be done numerically.

 

[laymanB]

Einstein's field equations relate the geometry of spacetime to the matter and energy distribution. You specify how the matter behaves and where it is at some point. You feed that into the EFEs and get sixteen simultaneous non-linear differential equations. If you've chosen a friendly setup many of those equations turn out to be 0=0 and you may be able to solve the rest. If not, you need a powerful computer.

Either way you end up with a metric tensor, which describes the geometry of spacetime given that distribution of matter. Schwarzschild started with a universe empty except for a spherically symmetric mass and derived the Schwarzschild metric, which works well for things like the solar system where 99%-ish of the mass is the Sun. Friedmann, Lemaitre, Robertson and Walker started with a universe completely filled with a same-everywhere mass distribution and came up with the FRW or FLRW metric, which works well on the scale where galaxies are dust grains.

There are a fair few known solutions, but an awful lot of interesting stuff (e.g. the binary mergers LIGO detects) can only be done numerically.

Thanks. That helps my understanding.

 

[StandardsGuy]

I'm not sure the question has been answered with all the pushback. I thought it took two massive objects moving near each other to produce gravitational waves. Is that correct? If you say it only takes one, can you prove that with observed data?