# Does non-gravitational acceleration produce waves?

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## Main Question or Discussion Point

In view of the observational equivalence of gravity and acceleration, does acceleration produce ripples in spacetime, similar to gravity waves?

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PeterDonis
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2019 Award
In view of the observational equivalence of gravity and acceleration, does acceleration produce ripples in spacetime, similar to gravity waves?
The short answer is "no", but the question itself appears to be based on a mistaken premise.

The "observational equivalence" is between being at rest relative to a rocket accelerating in flat spacetime (no gravity anywhere), and being at rest in a static gravitational field. In both of these cases, the acceleration being felt is not produced by "gravity". This is obvious in the flat spacetime case, since there is no gravity. But even in the curved spacetime case, being at rest in a gravitational field, what is holding you at rest is not "gravity" but whatever non-gravitational force is preventing you from freely falling. If you are standing on the Earth's surface, for example, the non-gravitational force of the Earth's surface pushing on you is what is holding you at rest.

In short, in both cases, the acceleration does not involve any change in the curvature of spacetime at all. And gravitational waves are changes in the curvature of spacetime that propagate at the speed of light. So if there is no change in the curvature of spacetime, there are no gravitational waves.

fresh_42
Mentor
In short, in both cases, the acceleration does not involve any change in the curvature of spacetime at all. And gravitational waves are changes in the curvature of spacetime that propagate at the speed of light. So if there is no change in the curvature of spacetime, there are no gravitational waves.
What I did not get here is that it is a mass that is accelerated. So wouldn't this cause tiny changes in spacetime and thus make a gravitational wave possible, even if it might not be measurable?

PAllen
2019 Award
What I did not get here is that it is a mass that is accelerated. So wouldn't this cause tiny changes in spacetime and thus make a gravitational wave possible, even if it might not be measurable?
Are you asking about treating the rocket case using GR rather than SR? Then, yes, in general, an accelerating rocket would generate (undetectable) gravitational radiation. [There are special cases where it wouldn't, e.g. the Kinnersly photon rocket solution. However, if you perturb the thrust pattern at all on that solution, you will get GW.] Some of the GW would be attributable to the mass of of they rocket payload.

Obviously, a body resting on a planet will not emit GW (the situation is static, so no propagation of anything).

Homework Helper
Thanks for the replies. If two black holes are rotating around each other at variable velocities (perhaps because of elliptical orbits), they would alternately be accelerating and decelarating. Wherever that is the case, could a fraction of what is measured by Ligo be explained by the acceleration?

PeterDonis
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2019 Award
it is a mass that is accelerated. So wouldn't this cause tiny changes in spacetime and thus make a gravitational wave possible, even if it might not be measurable?
If we are talking about a mass that produces non-negligible spacetime curvature being accelerated, we are talking about a different situation than the OP was referring to. If we are talking about "gravity and acceleration being equivalent", we are talking about the Equivalence Principle, which only applies in a small local patch of spacetime in which curvature can be ignored. Also, strictly speaking, the EP only applies to "test objects", which are idealized objects that produce zero spacetime curvature themselves. That was the scenario I was assuming in my response to the OP.

PeterDonis
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2019 Award
If two black holes are rotating around each other at variable velocities (perhaps because of elliptical orbits), they would alternately be accelerating and decelarating.
No, they wouldn't--at least, not in the sense of "acceleration" that is applicable to your OP, which is proper acceleration. The two black holes in your scenario would be in free-fall orbits around each other, with zero proper acceleration. (At least, they would when they were far enough away from each other; as they got closer and eventually merged, things would get more complicated, but there would still not be any simple sense in which either one would be accelerating in the sense of the EP.)

The "acceleration" you are talking about now is coordinate acceleration, which is not an invariant (proper acceleration is an invariant), and can't be the cause of anything (because only invariants can cause something else).

Wherever that is the case, could a fraction of what is measured by Ligo be explained by the acceleration?
No. See above.

fresh_42
Mentor
If we are talking about a mass that produces non-negligible spacetime curvature being accelerated, we are talking about a different situation than the OP was referring to. If we are talking about "gravity and acceleration being equivalent", we are talking about the Equivalence Principle, which only applies in a small local patch of spacetime in which curvature can be ignored. Also, strictly speaking, the EP only applies to "test objects", which are idealized objects that produce zero spacetime curvature themselves. That was the scenario I was assuming in my response to the OP.
Thank you. I was just asking because I thought that although unbelievably small it might be a non-zero solution. (I admit it's not really of physical interest.)

PeterDonis
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2019 Award
I was just asking because I thought that although unbelievably small it might be a non-zero solution.
PAllen is correct that, if we drop the assumption of the mass being a "test object", then accelerating it can produce gravitational waves. I was just pointing out that that is a different scenario than the one the OP was talking about.

pervect
Staff Emeritus
The absence of gravitational radiation in Kinnersley's photon rocket'' solution of Einstein's equations is clarified by studying the mathematically well-defined problem of point-like photon rockets in Minkowski space (i.e. massive particles emitting null fluid anisotropically and accelerating because of the recoil). We explicitly compute the (uniquely defined) [it]linearized[/it] retarded gravitational waves emitted by such objects, which are the coherent superposition of the gravitational waves generated by the motion of the massive point-like rocket and of those generated by the energy-momentum distribution of the photon fluid. In the special case (corresponding to Kinnersley's solution) where the anisotropy of the photon emission is purely dipolar we find that the gravitational wave amplitude generated by the energy-momentum of the photons exactly cancels the usual 1/r gravitational wave amplitude generated by the accelerated motion of the rocket. More general photon anisotropies would, however, generate genuine gravitational radiation at infinity. Our explicit calculations show the compatibility between the non-radiative character of Kinnersley's solution and the currently used gravitational wave generation formalisms based on post-Minkowskian perturbation theory.