The evaporation of charged black holes

TL;DR

This work analyzes the evaporation of highly charged black holes beyond the semiclassical regime by exploiting the Schwarzian action and its JT gravity realization in the near-horizon AdS2 throat. By combining one-loop gravitational corrections with exact Schwarzian correlators, it computes the corrected spectra for both neutral and charged Hawking radiation, including backreaction and metric fluctuations. The neutral-channel results reveal drastic low-temperature modifications that prevent superextremal emission and, for zero angular momentum, force emission to occur via entangled photon pairs, significantly slowing evaporation; in contrast, the Schwinger-rate for charged-particle emission remains essentially unchanged, with gravity fluctuations playing a subleading role. The paper then provides the full evaporation history of a large charged black hole, showing a punctuated evolution between bosonic and fermionic phases and detailing the implications for extremality, density of states, and possible observational tests with magnetic or highly charged black holes.

Abstract

Charged particle emission from black holes with sufficiently large charge is exponentially suppressed. As a result, such black holes are driven towards extremality by the emission of neutral Hawking radiation. Eventually, an isolated black hole gets close enough to extremality that the gravitational backreaction of a single Hawking photon becomes important, and the QFT in curved spacetime approximation breaks down. To proceed further, we need to use a quantum theory of gravity. We make use of recent progress in our understanding of the quantum-gravitational thermodynamics of near-extremal black holes to compute the corrected spectrum for both neutral and charged Hawking radiation, including the effects of backreaction, greybody factors, and metric fluctuations. At low temperatures, large fluctuations in a set of light modes of the metric lead to drastic modifications to neutral particle emission that -- in contrast to the semiclassical prediction -- ensure the black hole remains subextremal. Relatedly, angular momentum constraints mean that, close enough to extremality, black holes with zero angular momentum no longer emit individual photons and gravitons; the dominant radiation channel consists of entangled pairs of photons in angular-momentum singlet states. We also compute the effects of backreaction and metric fluctuations on the emission of charged particles. Somewhat surprisingly, we find that the semiclassical Schwinger emission rate is essentially unchanged despite the fact that the emission process leads to large changes in the geometry and thermodynamics of the throat. We present, for the first time, the full history of the evaporation of a large charged black hole. This corrects the semiclassical calculation, which gives completely wrong predictions for almost the entire evaporation history, even for the crudest observables like the temperature seen by a thermometer.

Figures (18)

• Figure 1: Comparison of the semiclassical prediction vs. quantum corrected Hawking radiation into the $\ell=1$ photon mode. (The quantum curve is the integrand from \ref{['eqn:photon_fullflux_kerrnewman']}; the semiclassical curve is the integrand from \ref{['eqn:photon_semiclassicalflux']}.) The energy flux per unit frequency is plotted for black holes in the microcanonical ensemble at initial energy $E_i=M-Q$ above extremality with fixed charge $Q$ and initial spin $j=0$. Left: A black hole far above the thermodynamic breakdown scale $(E_i = 10^5 E_\text{brk.})$. Quantum corrections are not important and the exact energy flux approaches the semiclassical prediction. Right: For a BH near the breakdown scale $(E_i = 2 E_\text{brk.})$, quantum corrections are important. The exact quantum answer cuts off the spectrum since the BH can't transition into states that don't exist. For photon emission from $j=0$ BHs the spectrum is cut off at $E_i-E_\text{brk.}$ due to angular momentum selection rules. Note that the scales of the two plots are very different due to the difference in energy above extremality.
• Figure 2: The evolution of the mass above extremality $M-M_0$ of a near-extremal black hole with initial charge $Q \gg Q_* \equiv 1.8 \times 10^{44} q$, as a function of time. Within the plot, time is scaled logarithmically within each straight-line segment. The emission of photons continuously decreases the mass, taking it below the breakdown scale $M-M_0 \sim E_\text{brk.}$ and reaching exponentially close to extremality. Below the breakdown scale, the quantum effects slow down the Hawking emission process. Pair production is exponentially suppressed, with positrons appearing with Poisson statistics on timescales $\delta t \sim e^{Q/Q_*}$. When a positron is made, it decreases the charge, increases the mass above extremality far above the breakdown scale, and causes the BH to transition from fermionic to bosonic and vice versa. The quantum-corrected Hawking radiation is different for bosonic and fermionic black holes below the breakdown scale $E_\text{brk.}$: bosonic black hole evaporation is dominated by di-photon decay, while fermionic black hole evaporation is dominated by single photon decay.
• Figure 3: A snapshot of the exterior of a near-extremal RN black hole. As for the Schwarzschild solution, there is a region far from the horizon where the Newtonian approximation holds (the 'Newtonian' region), and a region very close to the horizon where the gravitational field grows much more strongly than inverse-square (the 'Rindler' region). What's new for the RN solution is that the Rindler region forms only part of a long 'throat'. In the throat, the geometry is approximately $AdS_2 \times S^2$, so the area-radius $r$ is approximately constant, and, away from the Rindler region, the gravitational field is approximately constant. The closer the black hole is to extremality, the longer the throat.
• Figure 4: For any integer or half-integer angular momentum $j$, there exists a quasicontinuous density of black hole microstates for energies $E > Q+ E_{0}^j = Q + \frac{j (j+1)}{2} E_\text{brk.}$.
• Figure 5: Comparison of the semiclassical prediction vs. quantum corrected Hawking radiation into a massless scalar field. The energy flux per unit frequency is plotted for a black hole in the microcanonical ensemble at initial energy $E_i$ above extremality at fixed charge $Q$. Left: For a BH initially far above the thermodynamic breakdown scale $(E_i = 100 E_\text{brk.})$, quantum corrections are not important and the exact energy flux approaches the semiclassical prediction. Right: For a BH below the breakdown scale $(E_i = .1 E_\text{brk.})$ Schwarzian corrections are important and the distribution is no longer thermal. The exact Schwarzian answer cuts off the spectrum so particles with energy larger than the initial black hole energy, $\omega > E_i$, are not emitted. Note that the scales of the two plots are very different due to the difference in energy above extremality. The plot of the exact flux from the Schwarzian comes from the integrand of \ref{['eqn:scalarfinalflux']}, while the semiclassical flux is from \ref{['eqn:semiclassical_flux']}.