What is the significance of the recent LIGO result and its impact on textbooks?

[bcrowell]

The recent LIGO result seems likely to lead to a lot of rewriting of textbooks. Some topics that occur to me:

(1) Obviously it needs to be discussed in any GR textbook's discussion of gravitational waves.

(2) The fact that the waveform matches so well with GR calculations seems to be extremely strong evidence that black holes do exist and that they have the properties described in quantitative detail by GR. Previously, I don't think we had any observations that really probed radii close to the Schwarzschild radius. Now, I don't think there's much room left for theories in which runaway gravitational collapse stops short of the Schwarzschild radius. Also, this is a spectacular test of the Einstein field equations for very strong gravitational fields.

(3) For many decades, the better textbook treatments of SR have been trying to convince students that c is not to be interpreted as the speed of light. We've been able to say that c is a space-to-time conversion factor, or a universal speed limit, or the speed at which massless things travel. But until now, we didn't have a really good example, other than light, of something massless. Gluons aren't observed as free particles, and neutrinos turn out not to be massless. The aLIGO event makes gravitational waves into an excellent concrete example, and it also does support the prediction that gravitational waves travel at c. (The time delay is on the right order of magnitude, it has a statistically likely value, and it was not greater than the maximum allowed by GR. Also, the paper gives very tight limits on dispersion.)

 

[Vanadium 50]

Previously, I don't think we had any observations that really probed radii close to the Schwarzschild radius.

Orbits near galactic SMBH's.

 

[PeterDonis]

Orbits near galactic SMBH's.

These are outside the stable orbit limit, which is 3 times the Schwarzschild radius, aren't they? That's certainly close compared to what we can observe in the solar system, but it's only of the same order of closeness as, for example, the surface of a neutron star, which still isn't very close in terms of things like the time dilation factor. (The time dilation factor for an object in a circular orbit at 3 times the Schwarzschild radius is only ##1 / \sqrt{2} \approx 0.7##.)

I think bcrowell is referring to observations much closer than that, close enough, for example, to be inside the Buchdahl theorem limit for an object that can be in static equilibrium, which is 9/8 of the Schwarzschild radius. I don't know of any other observations that come anywhere close to that regime.

 

[PAllen]

These are outside the stable orbit limit, which is 3 times the Schwarzschild radius, aren't they? That's certainly close compared to what we can observe in the solar system, but it's only of the same order of closeness as, for example, the surface of a neutron star, which still isn't very close in terms of things like the time dilation factor. (The time dilation factor for an object in a circular orbit at 3 times the Schwarzschild radius is only ##1 / \sqrt{2} \approx 0.7##.)

I think bcrowell is referring to observations much closer than that, close enough, for example, to be inside the Buchdahl theorem limit for an object that can be in static equilibrium, which is 9/8 of the Schwarzschild radius. I don't know of any other observations that come anywhere close to that regime.

What about horizon imaging observations, and BH surface detection observations, which more and more rule out anything other than a horizon (macroscopically)? These have been posted several times here, so unless requested, I am not bothering to locate them right now.

 

[PeterDonis]

What about horizon imaging observations, and BH surface detection observations, which more and more rule out anything other than a horizon (macroscopically)?

Hm, you're right, those are probing at least near to the Buchdahl limit if not inside it.

 

[bcrowell]

Orbits near galactic SMBH's.

Objects like the star S2 and the gas cloud G2 are still thousands of Schwarzschild radii from Sag A* at periastron. The aLIGO waveform probes the physics all the way down to the Schwarzschild radius.

What about horizon imaging observations, and BH surface detection observations, which more and more rule out anything other than a horizon (macroscopically)? These have been posted several times here, so unless requested, I am not bothering to locate them right now.

My knowledge may be out of date, but the last I heard these observations had not succeeded in resolving the event horizon. I thought they were still an order of magnitude away from the Schwarzschild radius, although there were proposals to image the event horizon itself in the near future. Maybe the near future already happened while I wasn't looking...?

 

[PAllen]

My knowledge may be out of date, but the last I heard these observations had not succeeded in resolving the event horizon. I thought they were still an order of magnitude away from the Schwarzschild radius, although there were proposals to image the event horizon itself in the near future. Maybe the near future already happened while I wasn't looking...?

It is true that published Event Horizon Telescope results have not yet reached the horizon, but it is supposedly coming soon (a couple of years). This seems to be the among the most recent results from this collaboration:

http://arxiv.org/abs/1512.01220

However, I was mostly referring to the research program of the following, which have been linked here several times by Pervect:

http://arxiv.org/abs/astro-ph/0203089
http://arxiv.org/abs/gr-qc/0204080
http://arxiv.org/abs/astro-ph/0012452
http://arxiv.org/abs/astro-ph/0107387