Friday, May 26, 2017

Can we probe the quantization of the black hole horizon with gravitational waves?

Tl;dr: Yes, but the testable cases aren’t the most plausible ones.

It’s the year 2017, but we still don’t know how space and time get along with quantum mechanics. The best clue so far comes from Stephen Hawking and Jacob Bekenstein. They made one of the most surprising finds that theoretical physics saw in the 20th century: Black holes have entropy.

It was a surprise because entropy is a measure for unresolved microscopic details, but in general relativity black holes don’t have details. They are almost featureless balls. That they nevertheless seem to have an entropy – and a gigantically large one in addition – indicates strongly that black holes can be understood only by taking into account quantum effects of gravity. The large entropy, so the idea, quantifies all the ways the quantum structure of black holes can differ.

The Bekenstein-Hawking entropy scales with the horizon area of the black hole and is usually interpreted as a measure for the number of elementary areas of size Planck-length squared. A Planck-length is a tiny 10-35 meters. This area-scaling is also the basis of the holographic principle which has dominated research in quantum gravity for some decades now. If anything is important in quantum gravity, this is.

It comes with the above interpretation that the area of the black hole horizon always has to be a multiple of the elementary Planck area. However, since the Planck area is so small compared to the size of astrophysical black holes – ranging from some kilometers to some billion kilometers – you’d never notice the quantization just by looking at a black hole. If you got to look at it to begin with. So it seems like a safely untestable idea.

A few months ago, however, I noticed an interesting short note on the arXiv in which the authors claim that one can probe the black hole quantization with gravitational waves emitted from a black hole, for example in the ringdown after a merger event like the one seen by LIGO:
    Testing Quantum Black Holes with Gravitational Waves
    Valentino F. Foit, Matthew Kleban
    arXiv:1611.07009 [hep-th]

The basic idea is simple. Assume it is correct that the black hole area is always a multiple of the Planck area and that gravity is quantized so that it has a particle – the graviton – associated with it. If the only way for a black hole to emit a graviton is to change its horizon area in multiples of the Planck area, then this dictates the energy that the black hole loses when the area shrinks because the black hole’s area depends on the black hole’s mass. The Planck-area quantization hence sets the frequency of the graviton that is emitted.

A gravitational wave is nothing but a large number of gravitons. According to the area quantization, the wavelengths of the emitted gravitons is of the order of the order of the black hole radius, which is what one expects to dominate the emission during the ringdown. However, so the authors’ argument, the spectrum of the gravitational wave should be much narrower in the quantum case.

Since the model that quantizes the black hole horizon in Planck-area chunks depends on a free parameter, it would take two measurements of black hole ringdowns to rule out the scenario: The first to fix the parameter, the second to check whether the same parameter works for all measurements.

It’s a simple idea but it may be too simple. The authors are careful to list the possible reasons for why their argument might not apply. I think it doesn’t apply for a reason that’s a combination of what is on their list.

A classical perturbation of the horizon leads to a simultaneous emission of a huge number of gravitons, and for those there is no good reason why every single one of them must fit the exact emission frequency that belongs to an increase of one Planck area as long as the total energy adds up properly.

I am not aware, however, of a good theoretical treatment of this classical limit from the area-quantization. It might indeed not work in some of the more audacious proposals we have recently seen, like Gia Dvali’s idea that black holes are condensates of gravitons. Scenarios such like Dvali’s might be testable indeed with the ringdown characteristics. I’m sure we will hear more about this in the coming years as LIGO accumulates data.

What this proposed test would do, therefore, is to probe the failure of reproducing general relativity for large oscillations of the black hole horizon. Clearly, it’s something that we should look for in the data. But I don’t think black holes will release their secrets quite as easily.


  1. Another stark black hole (BH) attribute is its singularity to be exposed naked upon evaporation. LIGO Events GW150914 (35 + 30 sols) and GW151226 (14.2 and 7.5 sols) BH binaries inspiraled, merged, and rang down absent any angular momentum dance of their singularities merging - or not merging.

    Where was the singularities' binary wobble? Absent singularities, a BH is naught but a 2D+É› surface. One does not immediately fall "past" the event horizon in the falling reference frame. Things are much simpler than imagined. Perhaps a BH is not a matter condensate but a dimensional condensate.

  2. At the risk of going off topic, but since you brought this up, for a more empirically viable basis of this phenomenon, you might want to look at Giorgi Dvali's recent magnus opus on the axion(s) as a gravitational QCD unification - ArXiv 1705.06317.

  3. Uncle Al,
    how could a singularity hidden behind an event horizon emit gravitational waves (or anything else) to the outside universe during a black hole merger? Wouldn't the emission happen at the surface?

    would the ringdown start with some remaining mass distribution anomalies on the surface and end with the mass being distributed symmetrical? Or what does happen there and then?

  4. @Ambi Valent To an external observer, respective singularities whizzing about at a good fraction of lightspeed would require forever to fall through opposing event horizons. Total energy/c² emitted versus total mass involved, both events' binding energies were -4.6%. The events were two soap bubbles popping into one with a modest radius of curvature increase.

    I see two events whose observables were desperately ignored (though ignorance is also a good explanation).

  5. Uncle Al,
    what do you want to express?

    From my viewpoint, the singularities would indeed move very fast in the last stage of the inspiral phase - but then signals from them could not get out to outside observers.

    On the other hand, the last signals outside observers get from the centers of the objects would come from the time the two black holes were forming - and at that point they would have been much further apart and slower.

  6. @UA GW's are produced by the interaction of gravitational fields, not from dynamics of rearranging event horizons. Their gravitational influence extends many BH radii out into space. The question is when the classical (Newtonian) rapid in-spiral begins vs. when the GR time dilation becomes significant. Because these are fairly big BH masses, my guesstimate is the motion that produced the waves we detected took place well before time dilation was a big effect. I think you rely too much on visualizing. My teachers warned me not to do that. It's a trap. You can be misled by it, in fact, you seem to be quite often. In fact Bee has said something similar: trust the math, not the words. I would paraphrase it as you can't trust your intuition. That's what I think you do, and why your nebulous ideas are marginalized.

  7. "Uncle Al,
    what do you want to express?"

    Finally someone who goes after the Big Questions! Quantum gravity is child's play in comparison! :-)

  8. The ring down effect is intriguing to me.....per-sonifies the black characteristically I would think. Helps us to look at the nature of the black hole and points toward work done toward listening for gravitational wave production as in aluminum bars detection and not just LIGO. There is something analogistical once we sonify the perceptive way in which we are looking at measure.

  9. Inspiraling black hole binaries are end game orbital at a fat fraction of lightspeed, including their singularities. Singularities are separated and orbiting at merger. The summation violently wobbles when collapsing to equilibrium -quadrupolar big stuff absent from observation. No QM or information anomalies appear. Two merged soap bubbles, including negligible binding energies, model LIGO events

    Falsification is observation heretical to theory - the achiral Equivalence Principle versus chiral Einstein-Cartan dynamics (arXiv:1609.09275, DOI:10.1103/PhysRevD.95.104007). Empirical physical theory owes debts it refuses to pay. Progress seeks contradiction not confirmation. Look.

  10. Sonification as particularization and as radiation would leave signature value?


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