Damping of Gravitational Waves

[anorlunda]

Like many others, LIGO made me curious about gravitational waves. I found the paper:
Nonlocal Gravity: Damping of Linearized Gravitational Waves
http://arxiv.org/abs/1304.1769

In nonlocal general relativity, linearized gravitational waves are damped as they propagate from the source to the receiver in the Minkowski vacuum. Nonlocal gravity is a generalization of Einstein's theory of gravitation in which nonlocality is due to the gravitational memory of past events. That nonlocal gravity is dissipative is demonstrated in this paper within certain approximation schemes. The gravitational memory drag leads to the decay of the amplitude of gravitational waves given by the exponential damping factor exp (-t/\tau), where τ depends on the kernel of nonlocal gravity. The damping time τ is estimated for gravitational waves of current observational interest and is found to be of the order of, or longer than, the age of the universe.

I'm having difficulty understanding. Does that mean that damping is implicit in the terms of the tensors? Does it also mean that the energy in the wave just disappears in the non-energy conservation of GR?

I'm hoping that there is a non-tensor way to explain what causes the damping and where the energy goes. If not, I'll have to gnash my teeth and accept it.

If the decay time is of the order of the age of the universe, then the waves from almost every BH merger since the BB should still be zipping around for LIGO to detect, correct? That would be a large number of events.

 

[bcrowell]

Does that mean that damping is implicit in the terms of the tensors?

Do you realize that the paper is describing an obscure and nonstandard theory of gravity, not general relativity? General relativity says there is no such damping.

 

[anorlunda]

Do you realize that the paper is describing an obscure and nonstandard theory of gravity, not general relativity? General relativity says there is no such damping.

No I did not understand that. Thank you. I put too much trust in arxiv to be trustworthy.

So what about my last question. If there is no damping, then the waves from every BH merger event in the history of the universe should still be zipping around for LIGO to detect, correct?

 

[bcrowell]

No I did not understand that. Thank you. I put too much trust in arxiv to be trustworthy.

It's not a question of trusting arxiv, and there is nothing necessarily wrong with the paper. The abstract that you quoted explains straightforwardly that it's not a prediction based on GR.

So what about my last question. If there is no damping, then the waves from every BH merger event in the history of the universe should still be zipping around for LIGO to detect, correct?

Some have already passed through the earth. Others are beyond our cosmological event horizon and will never get to us.

 

[PeterDonis]

If there is no damping, then the waves from every BH merger event in the history of the universe should still be zipping around for LIGO to detect, correct?

No. Each BH merger happened at a particular event in spacetime. GWs from that event propagate along the future light cone of the event. That future light cone intersects our worldline here on Earth at one particular point; that's the event at which we detect the GWs from that merger. Once the waves have passed us, they're gone; they're moving away from us at the speed of light, so we'll never be able to catch up with them again.

 

[anorlunda]

No. Each BH merger happened at a particular event in spacetime. GWs from that event propagate along the future light cone of the event. That future light cone intersects our worldline here on Earth at one particular point; that's the event at which we detect the GWs from that merger. Once the waves have passed us, they're gone; they're moving away from us at the speed of light, so we'll never be able to catch up with them again.

I understand that. I didn't mean rencountering the same event, but rather independent events.

I presume that each supermassive BH the product of thousands or millions of merger events where a BH gobbles a star or another BH. There are many such supermassive BHs. Each event is detectable only once, but I expect that there must have been a trillion or so such events since stars began forming. Shouldn't the light cone of a thousand or so pass Earth each year?

Perhaps a partial answer might be that a BH-star merger makes waves too weak for LIGO to detect. Can we estimate the number of BH-BH merger events in the observable universe and the number we should expect to detect here per unit time?

 

[PeterDonis]

I didn't mean rencountering the same event, but rather independent events.

I understand that. But we will still see the GWs from each individual event only once. Damping has nothing to do with that.

Perhaps a partial answer might be that a BH-star merger makes waves too weak for LIGO to detect.

Yes. At LIGO's current sensitivity, as I understand it, it can only detect a very small fraction of all of the mergers that are expected to take place.

Can we estimate the number of BH-BH merger events in the observable universe and the number we should expect to detect here per unit time?

I believe the literature on LIGO includes such estimates, but I don't have a specific reference to point to right now.

 

[mfb]

Perhaps a partial answer might be that a BH-star merger makes waves too weak for LIGO to detect. Can we estimate the number of BH-BH merger events in the observable universe and the number we should expect to detect here per unit time?

Sure, and those estimates exist. They have huge uncertainties, so even with the 16 days of running time and a single observed event an estimate from LIGO results is probably more precise. Measuring those rates is one of LIGO's primary goals.

The black hole merger was quite massive, otherwise LIGO would not have been able to detect it at such a distance. To see events that are even more distant, they have to involve even heavier black holes, but at some point the frequency gets too low for LIGO (both larger masses and larger distance reduce the observed frequency). Most visible events are expected to be much closer, with smaller masses involved.

It gives a very promising outlook for improved precision measurements - increase the sensitivity by a factor of 3 and you get 27 times the event rate.