Testing General Relativity with Gravitational Waves

As we all wait for tomorrows LIGO press conference, I though that I could write a brief post on a relevant recent arXiv paper and say a couple of things on why tomorrows event is a big thing.

This is partially inspired by a twitter discussion with Leo after the paper came out.

Testing general relativity using golden black-hole binaries. (arXiv:1602.02453v1 [gr-qc]) https://t.co/vD3IViw8r4

— arXiv gr-qc (@arXiv_grqc) February 9, 2016

Since I am not a gravitational waves person, the discussion will not be any deep.

The resent paper, as you can see, is arXiv:1602.02453 (from Feb. 8 2016) titled: "Testing general relativity using golden black-hole binaries".

What the paper calls "golden black-hole binaries" are black hole binaries with a total mass in the range of $\sim 50M_{\odot}-200M_{\odot}$ that will produce a signal that all the way from the inspiral phase, to the merger phase and finally to the ringdown phase will be within the observing capabilities of ground based observatories like LIGO. And the proposal is that this sort of signals can be used to test General Relativity (GR) in the strong gravity regime. The proposed test is a null hypothesis test, i.e., the test assumes the validity of GR and then tests for consistency. The idea is that if the hypothesis, validity of GR, is correct, then the results that rely on the hypothesis should be consistent. If the results are not consistent, then the hypothesis is in trouble.

Since the test is all about consistency, it is critical to be able to observe all the phases of the binary system evolution, because the consistency check will be between the initial state, i.e., the two initial black holes that inspiral and merge, and the final state, i.e., the resulting object that will be initially perturbed and through the emission of gravitational waves it will relax to a final stationary state.

More specifically, the idea is the following. From the initial phase of the signal that covers the inspiral up to the merger, one could extract information about the masses $M_1$, $M_2$ and the spins $S_1$, $S_2$ of the two initial black holes. This can be done by match-filtering of simulated gravitational wave signals. One of the technics that are used to produce the simulated signals is that of the effective-one-body (EOB). This is an approach for describing the inspiral phase of binary black holes that was initially developed by A. Buonanno and T. Damour and has been further developed by them and their collaborators. The EOB description of inspirals is an analytic model of the inspiral and has been very successful and gives very accurate results that agree with the numerical simulations up to almost the final orbit before the plunge.

As I was saying, from the inspiral phase one can extract from the signal the masses and the spins. Now, from the final ringdown phase one in principle can extract from the frequency spectrum the mass $M_f$ and the spin $S_f$ of the resulting black hole, thanks to a huge amount of work that has been done on this. Of course, as Leo was pointing out yesterday, this calculation is model dependent, i.e., one would have to assume that the resulting object is a GR Kerr black hole for example.

@Vagelford @DrDa5id @gravitate_to_me no model-independent theory prediction of ringdown frequencies

— Leo C. Stein (@duetosymmetry) February 9, 2016

In any case, under this assumption one has a mass and spin for the resulting black hole. Therefore, from the signal we have a measurement of the properties of the two initial black holes and the properties of the final black hole. GR numerical simulations of mergers can tell us what will be the end state of the merger given the initial state, i.e., the two initial orbiting black holes. Therefore one could predict the end state properties and compare them to the properties measured from the ringdown. And this is the null hypothesis test since throughout the validity of GR is assumed.
The authors finally propose that even if GR might not be tested with high precision from one signal, the combined statistics from multiple events could place strong constrains on deviations from GR.


And this is all I can tell about this paper. Any insights from the experts would be most welcome.

I only want to end with a final note. The actual detection of gravitational waves will of course be a significant event in itself but it will not be the most important aspect of the thing. The most important aspect of the actual measurement of gravitational waves will be the amazing physics and astrophysics and cosmology that we will be able to do with them, testing our theories beyond anything we have managed to test so far (as this preprint describes for example). Radio waves, X-rays and $\gamma$-rays revolutionised astronomy, changed our view of the universe and opened our eyes to an amazing plethora of phenomena that furthered our understanding of how the cosmos works. Gravitational waves have the potential to provide us with an even more spectacular view.

Cheers.