Gravitational waves affected by gravity?

[DuckAmuck]

So we know that in GR electromagnetic waves have their trajectories effected by the gravity of stars and planets. But how about gravitational waves. Are their trajectories altered by gravity? If so, would this imply that gravitons are self-interacting if they exist?

 

[PeterDonis]

Are their trajectories altered by gravity?

Yes.

would this imply that gravitons are self-interacting if they exist?

Yes.

 

[newjerseyrunner]

I think mathematically, they'd have to, but it couldn't have been observed yet. We'll need a very specific set of circumstances to occur. First, our gravity wave telescopes will have to be able to pinpoint the source of a wave, and the wave must have been produced by something that emits light, and we can see it with regular telescope. Looking far off into space is like looking through moving water, it's distorted because of the geodesics the light travels due to matter and dark matter. If gravity waves follow geodesics, then the source will appear to be in the same location as the source of light. If they don't line up perfectly, that means that the light and gravity took different paths to Earth. That would imply that our equations are wrong.

 

[Chronos]

To the best of my knowledge, the jury is still out on these questions. IIRC, Peter, you expressed a somewhat different opinion here: https://www.physicsforums.com/threads/does-gravity-gravitate.768604/

 

[newjerseyrunner]

Wait. If gravity gravitates around geodesics, shouldn't gravity not be able to escape a black hole and cause them to be basically self contained?

 

[mfb]

There is nothing that would have to escape for a black hole to exist.

 

[newjerseyrunner]

There is nothing that would have to escape for a black hole to exist.

I'm probably just ignorant of how the theoretical gravity boson would work. My assumption is that two particles would be attracted to each other by exchanging a graviton, the same way that they would interact electromagnetically by exchanging a photon. Is that correct? If the gravity boson is self interacting and follows the same geodesics as the photons, how could an interaction happen between the black hole and another object? Wouldn't the boson have no path that leads outwards?

I agree that if gravitons exist, they don't prevent a black hole from forming. What I'm saying is that once the hole is formed, if gravitons would not be able to interact with anything beyond the event horizon and essentially it'd stop pulling on everything else. Wouldn't you also be able to have particles made purely out of self-attracting bosons? The graviton equivalent of a gluball?

 

[Chronos]

I suspect Einstein was right all along: gravity is strictly a consequence of spacetime geometry - no gauge boson required.

 

[newjerseyrunner]

I suspect Einstein was right all along: gravity is strictly a consequence of spacetime geometry - no gauge boson required.

I suspect that too.

 

[bapowell]

I suspect Einstein was right all along: gravity is strictly a consequence of spacetime geometry - no gauge boson required.

But these are not mutually exclusive viewpoints: the gauge boson in a gauge theory is associated with the connection on the fibre bundle, which is also a geometrical object. Take electromagnetism: we have a gauge boson, the photon, which arises mathematically as the connection on the U(1) bundle, i.e. it defines parallel transport in the internal U(1) space.

 

[newjerseyrunner]

But these are not mutually exclusive viewpoints: the gauge boson in a gauge theory is associated with the connection on the fibre bundle, which is also a geometrical object. Take electromagnetism: we have a gauge boson, the photon, which arises mathematically as the connection on the U(1) bundle, i.e. it defines parallel transport in the internal U(1) space.

I'm still trying to understand how that's possible if we know that black holes exist and pull on everything around them. If a black hole has intense enough gravity the gravitons themselves would not be able to escape and would therefore not be able to interact with anything else? How can a boson come from the central mass, go past the event horizon, and interact with a passing particle?

 

[weirdoguy]

My assumption is that two particles would be attracted to each other by exchanging a graviton, the same way that they would interact electromagnetically by exchanging a photon. Is that correct?

AFAIK, by exchanging virtual photon, and I think that this changes the case dramatically. Virtual particles are not real particles (wow), they're just a mathematical tool used in perturbative approach to QFT. I think one should distinguish between gauge fields and excitations of those. Gravitons may be trapped inside BH, but that doesn't mean that there is no graviton filed outside BH.

 

[PeterDonis]

To the best of my knowledge, the jury is still out on these questions.

I'm not sure what you mean. I'm not aware of any uncertainty in mainstream GR about the first question; if we model gravitational waves as fluctuations of spacetime curvature on a background spacetime geometry, their trajectories will follow the background spacetime geometry. That means those trajectories are "affected by gravity".

The second question is ok because it has a caveat: "if they exist". In other words, it's a hypothetical: assuming gravitons do exist, are they self-interacting? The answer to this is obviously yes: the theory of a spin-2 field is nonlinear, so the field is self-interacting.

Basically, it looks to me like both of these questions can be put in the form: are the equations governing gravity nonlinear? The answer to that is yes.

IIRC, Peter, you expressed a somewhat different opinion here

As I understand the OP's questions, they are interpreting "gravity" in the way that I said would give a "yes" answer to the question "does gravity gravitate?" in that series of posts (see above). Btw, from the shameless plug department , updated versions are now posted as Insights posts; the link below is to the third, which talks specifically about gravitational waves, and has links to the other two:

https://www.physicsforums.com/insights/gravity-gravitate-part-3-wave/#toggle-id-1

 

[PeterDonis]

If gravity gravitates around geodesics, shouldn't gravity not be able to escape a black hole and cause them to be basically self contained?

If a black hole has intense enough gravity the gravitons themselves would not be able to escape and would therefore not be able to interact with anything else?

Read these:

http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_gravity.html

https://www.physicsforums.com/threads/how-does-gravity-get-out-of-a-black-hole.856841/

Also there is another way of looking at it: what determines the gravity you feel at a given event in spacetime? If we agree that causal influences can't travel faster than light, then any gravity you feel at a given event must be coming from sources in the past light cone of that event. But the interior of a black hole is not in your past light cone if you're outside the hole. So the gravity you feel can't be coming from inside the hole. It must be coming from the matter in the far distant past that originally collapsed to form the hole. That matter is in your past light cone, so it can affect the gravity you feel.

Note that this is true for ordinary objects as well. For example, the gravity the Earth feels from the Sun is not coming from the Sun "right now"; it's coming from the Sun 500 seconds ago (if we adopt coordinates in which the Sun, or more precisely the barycenter of the solar system, is at rest), i.e., from the presence of the matter in the Sun in our past light cone here on Earth. But the situation is almost static, so that is almost the same as having the gravity the Earth feels determined by the Sun "right now". The small differences show up in things like the perihelion shift of the planets. Similarly, since the black hole is static, or almost static, having your gravity determined by the matter in your past light cone that collapsed to form the hole is almost the same as having it determined by the hole "right now". But there are small differences, which would show up if we made the appropriate measurements.

 

[newjerseyrunner]

@PeterDonis great explanation, thanks.

 

[Chronos]

I'm just a bit uncomfortable with notion of the gravitational field of a black hole as a fossil field - i.e., a relic of the matter field present before the black hole formed. I don't see how this would work for an inspiraling black hole binary system. How would the system orbit decay via gravitational wave emission from a relic matter field? I would naively expect it to decay via energy being carried off from the current matter field configuartion. Would you not also expect a Shapiro delay in GW's emittedy by a binary black hole system similar to PSR J0737-3039? re: http://www.jb.man.ac.uk/pulsar/doublepulsarcd/papers/physworld.pdf. I sense causality issues.

 

[timmdeeg]

I'm just a bit uncomfortable with notion of the gravitational field of a black hole as a fossil field - i.e., a relic of the matter field present before the black hole formed. I don't see how this would work for an inspiraling black hole binary system. How would the system orbit decay via gravitational wave emission from a relic matter field? I would naively expect it to decay via energy being carried off from the current matter field configuartion.

I think it doesn't matter if the two masses of the binary system are neutron stars or black holes. The energy radiated away corresponds to the decreasing gravitational potential in both cases. I don't see how a relic matter field could be involved, but I'm not sure if I'm missing something.

 

[PeterDonis]

I'm just a bit uncomfortable with notion of the gravitational field of a black hole as a fossil field - i.e., a relic of the matter field present before the black hole formed.

It's not a "relic" any more than the field at the Earth due to the Sun is a "relic". Both are due to the presence of stress-energy in the past light cone.

How would the system orbit decay via gravitational wave emission from a relic matter field?

Once again, spacetime curvature, which includes gravitational waves since those are waves of spacetime curvature, is ultimately due to the presence of stress-energy in the past light cone. If the system is a black hole binary, then the configuration of the stress-energy in the past light cone is such as to produce spacetime curvature that describes a black hole binary, including the gravitational waves it emits.

Would you not also expect a Shapiro delay in GW's emittedy by a binary black hole system

I'm not sure how the Shapiro delay is relevant here. The delay is observed in radiation that is emitted from a source far away from the gravitating system, then pass close to it, then come out to a detector far away. We are talking about radiation that is emitted from the gravitating system.

I sense causality issues.

I would suggest reading up on the initial value formulation of GR. It is a proven theorem that, given reasonable initial conditions, the Einstein Field Equation has a well-posed initial value problem. In the case of a black hole binary, the initial conditions would be the original configuration of matter fields on a spacelike hypersurface that describe two objects (such as stars) that will end up collapsing into the two black holes orbiting each other. The existence of a well-posed initial value problem is what ensures that the statements I have made about the spacetime curvature at a given event being due to sources in the past light cone are justified.

I would also recommend reading up on ADM energy and Bondi energy for an isolated system. Both of these are well-defined integrals that can be evaluated at infinity (spacelike infinity for ADM energy, future null infinity for Bondi energy), and the difference between them is precisely the energy carried away by radiation. This is a well-studied subject and the statements I am making are not at all controversial in GR.

 

[newjerseyrunner]

Wait, the gravity from the sun taking 500 seconds is not like the gravity coming from a black hole. The lag is purely because of distance and the speed at which gravity works, but from the mass of the sun, to the earth, that gravity is traveling through essentially flat space (compared to a black hole anyway.) Look at my diagram (sorry about my handwriting.)

On the left is the sun, which is the gravity source. The "graviton" would travel from the gravity source, through space, to the earth. It's affects would then be felt.

On the right, you have a black hole. You have the gravity source in the middle of the black hole and a planet orbiting it. You have the flat(ish) space between the event horizon and the planet, but there is a gap. How does the gravity come from the gravity source all the way in the center of the black hole, through all that space that's curved so much that all geodesics point inwards?

In both diagrams, the "path" of gravity is the dotted line. How does gravity get through the part I've labeled as "very curved space?" What is the path from the gravity source in the center of the hole, to the edge of the Schwarzschild radius?

Is it because from our point of view, as objects approach the event horizon, they stop in time? Is the gravity source felt by orbiting objects from the surface of the black hole and not the singularity inside?

 

[PeterDonis]

the gravity from the sun taking 500 seconds is not like the gravity coming from a black hole. The lag is purely because of distance and the speed at which gravity works

And the same is true in the black hole case; the gravity you feel hovering above the hole comes from the stress-energy in your past light cone, i.e., from the matter that collapsed to form the hole. The only difference is that the matter might have collapsed millions or billions of years ago--but because of gravitational time dilation, light signals from the collapsing matter just before it fell below the horizon can take that long to get out to you. The same is true of "gravity signals" if you assume that gravity propagates at the speed of light (which is what GR predicts although we have not directly measured this).

You have the gravity source in the middle of the black hole

No, you don't. Your assumptions about the geometry of spacetime in the interior of a black hole are not correct. The black hole is vacuum inside. The singularity at the center, $r = 0$, is not, strictly speaking, part of spacetime at all; but considered as a boundary of spacetime, it is in the future--i.e., it is a moment in time (which is in the future of anyone inside the horizon), not a place in space.

How does gravity get through the part I've labeled as "very curved space?

It doesn't. Once again: the gravity is not coming from inside the hole. It is coming from the matter that collapsed in the far past to form the hole. Please take a big step back and think very carefully about what that means.

Is it because from our point of view, as objects approach the event horizon, they stop in time?

There is a sense in which this is sort of getting at a piece of the answer (see my comment above about how long light takes to get out to you from close to the horizon), but it has nothing to do with objects "stopping in time", it has to do with the propagation of light (or gravity) near the horizon.

Is the gravity source felt by orbiting objects from the surface of the black hole and not the singularity inside?

Neither. I've already said where the gravity comes from. Please read what I posted again, carefully.

 

[newjerseyrunner]

Interesting. The matter from the past affecting objects in the present is strange, but I think I'm starting to understand it.

Follow up though. As the black hole evaporates, how does the effect of that past matter dissipate? Or is that one of the issues with the black hole information paradox? I imagine it being released as the black hole shrinks that "future" singularity comes closer and closer to the present?

 

[PeterDonis]

As the black hole evaporates, how does the effect of that past matter dissipate?

Heuristically, as the hole evaporates, its horizon radius decreases, so the gravitational time dilation at a fixed radius gets smaller. That means there is less and less effect of past matter still "waiting" to propagate out to that radius. By contrast, if the hole is static (not evaporating, i.e., the idealized classical GR case), gravitational time dilation at a given radius is constant.

as the black hole shrinks that "future" singularity comes closer and closer to the present?

No. First of all, we're not even sure if the singularity is still there once quantum effects are taken into account (which they have to be if we're talking about black hole evaporation). Second, even if the singularity is still there, it is only in the future for an observer inside the horizon; it isn't for an observer who stays outside the horizon. So there is no sense in which it "gets closer to the present" for an observer outside the horizon. (It does for an observer inside the horizon, but only because that observer is falling into the singularity just by moving into the future, and that is true whether the hole is evaporating or not.)

 

[ProfChuck]

Light waves and gravitational waves are both bent by gravitational fields. This is a consequence of the equivalence between gravitational mass and inertial mass and the fact that the speed of light is finite. The mass-energy value of photons have nothing to do with the phenomena except possibly as a small second order effect which can influence local space-time curvature. If you think in terms of Einsteins spacecraft laboratory thought experiment you will see that a beam of light is bend downward if the spacecraft is accelerating simply because of the dynamics of the coordinate system.

 

[PeterDonis]

This is a consequence of the equivalence between gravitational mass and inertial mass and the fact that the speed of light is finite.

Actually, if you just base your prediction of light bending on the equivalence principle (i.e., analyzing how light paths are bent in an accelerating laboratory in flat spacetime), you will get an answer that is only half the correct answer. To get the other half, you need to take into account the curvature of space around the massive object that is bending the light.

It's also not really clear that the EP reasoning would apply to gravitational waves, since they are waves of spacetime curvature, and the EP by definition only applies in a small local patch of spacetime where the effects of spacetime curvature are not detectable.

 

[ProfChuck]

If gravitational waves propagate at the speed of light, and both theory and recent measurement strongly indicate that they do, then they should be curved by space-time. Einstein's space laboratory thought experiment assumed that the lab was very small as compared to the size of a gravitational mass. In this way gravitational gradient and gravitational point source and near field effects would not enter into the experiment. Under these conditions local space-time is indistinguishable from being flat. In the accelerating laboratory two falling objects path will only deviate from parallel due to their mutual attraction. In a planetary field they will also be drawn together by the fact that their velocity vectors meet at the center of the attracting mass. Even so, EP and the finite velocity of light were pivotal factors in the development of both SR and GR.

 

[PeterDonis]

If gravitational waves propagate at the speed of light, and both theory and recent measurement strongly indicate that they do, then they should be curved by space-time.

Yes, I already agree with that, as I said in post #2 of this thread. I'm simply pointing out that you can't use the equivalence principle as a basis for this conclusion for gravitational waves, and even using the EP to draw the conclusion for light doesn't give you the correct quantitative answer.

Einstein's space laboratory thought experiment assumed that the lab was very small as compared to the size of a gravitational mass. In this way gravitational gradient and gravitational point source and near field effects would not enter into the experiment. Under these conditions local space-time is indistinguishable from being flat. In the accelerating laboratory two falling objects path will only deviate from parallel due to their mutual attraction. In a planetary field they will also be drawn together by the fact that their velocity vectors meet at the center of the attracting mass. Even so, EP and the finite velocity of light were pivotal factors in the development of both SR and GR.

All of this is true, but it does not contradict or refute what I said in my previous post, and repeated above.

 

[Jenab2]

Gravity waves create space-distortion spectra in time that begins like a low-frequency, low-amplitude wiggle, with both frequency and amplitude reaching a peak (a crescendoed chirp) and then a rapid fade-out. The masses of the interacting objects (e.g. black holes) determines the structure of the gravity waveform. If the same waveform is detected at more than one time by a LIGO-like detector, it could mean that the signal was gravitationally lensed, with duplicate signals taking paths of different length to reach the detector.