What happens to the event horizon of two black holes if they merge? Might gravitational

waves emitted from such a merger tell us if Einstein’s theory of general relativity

is wrong? Yes, they might. But it’s unlikely. In this video, I will explain why. In more

detail, I will tell you about the possibility that a gravitational wave signal from a black

hole merger has echoes.

But first, some context. We know that Einstein’s theory of general relativity is incomplete.

We know that because it cannot handle quantum properties. To complete General Relativity,

we need a theory of quantum gravity. But progress in theory development has been slow and experimental

evidence for quantum gravity is hard to come by because quantum fluctuations of space-time

are so damn tiny. In my previous video I told you about the most promising ways of testing

quantum gravity. Today I want to tell you about testing quantum gravity with black hole

horizons in particular.

The effects of quantum gravity become large when space and time are strongly curved. This

is the case towards the center of a black hole, but it is not the case at the horizon

of a black hole. Most people get this wrong, so let me repeat this. The curvature of space

is not strong at the horizon of a black hole. It can, in fact, be arbitrarily weak. That’s

because the curvature at the horizon is inversely proportional to the third power of the black

hole’s mass. This means the larger the black hole, the weaker the curvature at the horizon.

It also means we have no reason to think that there are any quantum gravitational effects

near the horizon of a black hole. It’s an almost flat and empty space.

Black holes do emit radiation by quantum effects. This is the Hawking radiation named after

Stephen Hawking. But Hawking radiation comes from the quantum properties of matter. It

is an effect of ordinary quantum mechanics and not an effect of quantum gravity.

However, one can certainly speculate that maybe General Relativity does not correctly

describe black hole horizons. So how would you do that? In General Relativity,

the horizon is the boundary of a region that you can only get in but never get out. The

horizon itself has no substance and indeed you would not notice crossing it. But quantum

effects could change the situation. And that might be observable.

Just what you would observe has been studied by Niayesh Afshordi and his group at Perimeter

Institute. They try to understand what happens if quantum effects turn the horizon into a

physical obstacle that partly reflects gravitational waves. If that was so, the gravitational waves

produced in a black hole merger would bounce back and forth between the horizon and the

black hole’s photon sphere. The photon sphere is a potential barrier at about one and a

half times the radius of the horizon. The gravitational waves would slowly leak during

each iteration rather than escape in one bang. And if that is what is really going on, then

gravitational wave interferometers like LIGO should detect echoes of the original merger

signal.

And here is the thing! Niayesh and his group did find an echo signal in the gravitational

wave data. This signal is in the first event ever detected by LIGO in September 2015. The

statistical significance of this echo was originally at 2.5 σ. This means roughly one-in-a-hundred

times random fluctuations conspire to look like the observed echo. So, it’s not a great

level of significance, at least not by physics standards. But it’s still 2.5σ better than

nothing.

Some members of the LIGO collaboration then went and did their own analysis of the data.

And they also found the echo, but at a somewhat smaller significance. There has since been

some effort by several groups to extract a signal from the data with different techniques

of analysis using different models for the exact type of echo signal. The signal could

for example be dampened over time, or it’s frequency distribution could change. The reported

false alarm rate of these findings ranges from 5% to 0.002%, the latter is a near discovery.

However, if you know anything about statistical analysis, then you know that trying out different

methods of analysis and different models until you find something is not a good idea. Because

if you try long enough, you will eventually find something. And in the case of black hole

echoes, I suspect that most of the models that gave negative results never appeared

in the literature. So the statistical significance may be misleading.

I also have to admit that as a theorist, I am not enthusiastic about black hole echoes

because there are no compelling theoretical reasons to expect them. We know that quantum

gravitational effects become important towards the center of the black hole. But that’s

hidden deep inside the horizon and the gravitational waves we detect are not sensitive to what

is going on there. That quantum gravitational effects are also relevant at the horizon is

speculative and pure conjecture, and yet that’s what it takes to have black hole echoes.

But theoretical misgivings aside, we have never tested the properties of black hole

horizons before, and on unexplored territory all stones should be turned. So, that’s

the status of the search for black hole echoes. As usual, you find references in the information

below the video. Thanks for watching. And don’t forget to subscribe.