Charged Black Holes Emit Charged Particles, and Quantum Gravity Corrections Barely Matter
Quantum corrections to near-extremal black holes drastically rewrite the Hawking spectrum for photons and gravitons, but switch to charged particles and the corrections nearly vanish — because the particles are mostly produced in the throat, far from the horizon, where they cannot feel the metric fluctuations near the horizon.
The argument · tap a timestamp to hear it
Near-extremal black holes are actually quantum objects
In classical general relativity a black hole is characterized by three parameters — mass M, charge Q, angular momentum J — and solutions exist only when M is greater than or equal to Q; the case of exact equality is an extremal black hole, and near-equality is a near-extremal black hole. Over the past few years, via the Euclidean gravitational path integral, it was found that near-extremal black holes receive very large fluctuations from the quantum metric, and many textbook properties are thereby rewritten. This is precisely the motivation for this talk: since so many properties have changed, the standard story of Hawking radiation should be run through again as well.
— Mykhaylo UsatyukThe Schwarzian mode is one-loop exact
Write the metric as a classical solution plus fluctuations and the gauge field as a classical field plus fluctuations, then expand the action, and the fluctuations can be computed. In the past this was done only at quadratic order, to compute the logarithmic correction to the entropy; the new development is the identification of a class of special metric fluctuations confined deep in the ADS2 throat, namely the Schwarzian modes. Their effective action is proportional to temperature divided by some energy scale, vanishes at zero temperature, and contributes enormously when the temperature is far below that scale. More crucially, this action as a whole is the Schwarzian theory, and it is one-loop exact: computing only the quadratic terms automatically includes all higher-order interaction terms.
— Mykhaylo UsatyukThe neutral-particle spectrum is rewritten by quantum corrections
For the S-wave of a massless scalar, the Hawking formula gives the energy flux. Taking the initial energy to be 100 times the breaking scale, the quantum rate and the semiclassical curve nearly coincide; but pushing the initial energy down to one tenth of the breaking scale, the two curves diverge enormously, and the quantum rate does not allow the black hole to radiate away more energy than the amount by which it exceeds extremality. This is the evidence that quantum gravity corrections matter in the neutral-particle story, and it is the benchmark against which charged particles are later compared.
— Mykhaylo UsatyukCharged particles were previously incalculable because the dimension goes complex
In parameter space, in the region where both mass and charge are large (the QED region) as well as in the massless charged region, the scaling dimension of the scalar field in ADS2 becomes complex, the techniques used for neutral particles do not apply, and this is why charged particles long remained incompletely understood. The only corner where similar techniques carry over is the ‘lightly charged field’ corner: add a tiny charge to the massless field so that the particle charge times the black hole charge is far less than 1, and the scaling dimension is about 1. In this corner, adding a little charge makes the deviation from the semiclassical answer shrink dramatically.
— Mykhaylo UsatyukThe Hawking calculation and the Schwinger calculation are equivalent
There are two perspectives in the literature for computing black hole electron production: one is Hawking-style, canonically quantizing on a curved background and evaluating the particle number operator at infinity; the other is Schwinger-style, treating the black hole as a background electric field and computing pair production via the Schwinger mechanism. The former is the correct calculation and implicitly includes Schwinger pair production, but it is extremely hard; the latter is far easier. This talk proves that as the temperature goes to zero, the Hawking calculation and the Schwinger calculation give nearly identical results, the only difference being that Hawking decomposes in spherical angular momentum modes with quantized angular momentum, whereas Schwinger uses a flat-space approximation with no quantized angular momentum.
— Mykhaylo UsatyukOne electron kicks the black hole back into the safe zone
The backreaction is very violent: if the black hole sits in the near-extremal, highly quantized region, then emitting a single electron (which carries away a large amount of energy and charge) lands the black hole's final state back in the completely safe semiclassical region. This explains why quantum gravity corrections to charged-particle emission do not matter — the produced particle itself pushes the system out of the quantum region.
— Mykhaylo UsatyukThe superradiance boundary is where particles just barely cannot escape
Reinterpreting the Hawking spectrum in the Schwinger picture, it splits into three segments. Near the superradiance boundary (green region): in the point-particle approximation, a particle produced too close to the horizon falls in and cannot escape, so the rate drops sharply to zero at the superradiance boundary; the peak corresponds exactly to the position of the point particle's unstable minimum, push a little to the left and it escapes, push a little to the right and it falls into the black hole. Middle purple region: particles are produced in the long ADS2 throat or the flat-space part, and Schwinger is an excellent approximation. Leftmost red region: particles would have to be produced at infinity in an infinitely weak electric field, the rate is essentially zero, and so an essential singularity appears.
— Mykhaylo UsatyukQuantum corrections cannot reach most of the particles
In a certain gauge the metric fluctuations are localized near the Euclidean horizon, whereas charged particles are mostly produced in the throat or even farther out in the flat-space region, far from these fluctuations, unable to feel them, so the rate is naturally unaffected. What might receive large corrections is the green region hugging the superradiance boundary, but that region is small and its contribution to the total rate is limited. The author states explicitly that tools are currently lacking to compute precisely how the green-region rate is modified, so no exact answer can be given.
— Mykhaylo UsatyukIn their own words · checked verbatim
near extreal black holes behave as very quantum mechanical objects
Mykhaylo Usatyuk1:20
if we studied these modes exactly at zero temperature on the zero temperature black hole we'd find that they're exact zero they have no action
Mykhaylo Usatyuk12:30
we're going to show that the Hawking calculation here exactly matches the Schwinger calculation
Mykhaylo Usatyuk33:27
This black hole is now in a very safe semiclassical regime. So one electron gets you far away from this very quantum nature.
Mykhaylo Usatyuk43:34
Schwinger and Hawking are both semicclass so we showed that two semiclass calculations are equivalent right And now we're going to use the intuition from the semiclassical calculation to explain why quantum gravity effects uh would likely be unimportant. So it's an extrapolation.
Mykhaylo Usatyuk59:23
Many textbook properties of near external black holes are modified but not charged particle production.
Mykhaylo Usatyuk1:02:28
Figures
| Initial energy at which quantum corrections to neutral particles are significant | 1/10 of the breaking scale | 20:50 |
| Initial energy at which the neutral-particle semiclassical and quantum curves coincide | 100 times the breaking scale | 20:50 |
| Particle charge times black hole charge in the lightly charged field corner | 1/10 | 26:56 |
| Characteristic energy of charged-particle emission | about 10^19 GeV | 36:28 |
Glossary
- near extremal black hole
- A black hole whose mass approaches the charge lower bound M=Q, with extremely low temperature and significant quantum fluctuations.
- Schwarzian modes
- Special metric fluctuations localized deep in the ADS2 throat, with a one-loop exact action.
- superradiance
- In a charged black hole, the emission boundary when the particle frequency is below the charge times the horizon gauge potential.
- Schwinger pair production
- The mechanism by which positive-negative particle pairs are spontaneously produced from the vacuum in a constant electric field.
- worldline instanton
- A semiclassical method for computing the Schwinger pair production rate, requiring the instanton scale to be far smaller than the scale over which the field varies.
How to listen
Graduate students and postdocs working on black hole information, quantum gravity, or ADS/CFT; theoretical physicists who want to know the latest on quantum corrections to near-extremal black holes.
The outline and background introduction at the start, 0:00-5:23; go straight to the substance from 5:23.