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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.