The evaporation of charged black holes (2411.03447v1)

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.

• The paper demonstrates how quantum gravitational corrections modify neutral and charged particle emissions from near-extremal black holes.
• It employs gravitational instanton techniques and Schwinger pair production to derive emission rates when semiclassical predictions fail.
• The study reveals that despite Schwarzian fluctuations, charged emission rates remain largely unaffected, offering new insights into black hole entropy and thermodynamics.

Analysis: The Evaporation of Charged Black Holes

This paper presents a comprehensive paper of the evaporation mechanisms of charged black holes, focusing on the quantum gravitational corrections to Hawking radiation and the emission of charged particles in these contexts. The analysis builds on semiclassical physics, but progresses into quantum theory of gravity when the semiclassical approximation breaks down.

Key Findings

1. Hawking Radiation in Charged Black Holes: The paper investigates both neutral and charged particle emission from near-extremal charged black holes. The emission rate of neutral particles is derived using a quantum gravitational perspective when semiclassical predictions fail at low temperatures.
2. Gravitational Instanton and Pair Production: The gravitational instanton technique is employed to estimate the rate of charged particle emission. In particular, Schwinger pair production near the event horizon plays a critical role, leading to suppressed rates for very large charges. It is found that pair production typically occurs far from extremality, resulting in highly relativistic particles carrying significant kinetic energy away from the black hole.
3. Quantum Gravity Effects: Utilizing the Schwarzian theory in the context of AdS$_2$/CFT correspondence, the paper explores quantum effects modifying the emission processes at low temperatures. These corrections become significant below the breakdown scale $E_{\text{brk}}$, where the semiclassical approximation ceases to be valid.
4. Density of States and Entropy Considerations: Near-extremal charged black holes exhibit a complex behavior where entropy increases due to Hawking radiation. The entropy difference between the initial and final states after charged particle emission correlates with the observed tunneling rates.
5. Effect of Schwarzian Fluctuations: The paper reveals that the effects of Schwarzian modes—arising from fluctuations in the near-horizon region—do not affect the charged particle emission rate, which remains congruent with semiclassical predictions despite the backreaction and gravitational interaction corrections.

Implications and Future Directions

The implications of this research extend toward understanding black hole thermodynamics within a quantum gravity framework. The discrepancies between semiclassical approximations and full quantum calculations hint at a rich physics that awaits exploration with effects showing how black holes approach extremality and how information might be conserved within quantum theories of gravity.

Future research could investigate other theories of gravity beyond Einstein-Maxwell dynamics, or explore these effects in higher-dimensional scenarios or black holes with other charges like magnetic monopoles. Additionally, understanding the precise role of quantum fluctuations in modifying the charged particle emission, especially in the presence of complex interaction effects, could provide deeper insights into black hole evaporation dynamics.

Furthermore, the interplay between gravitational and quantum effects in black hole thermodynamics might offer observational prospects, although current technological limitations make direct observation challenging. The highly controlled theoretical results from this work provide a blueprint for interpreting potential future observational data from highly charged astrophysical black holes, should they be found and observed.

This paper thus serves as a significant contribution to the field of quantum gravity, particularly in the exploration of near-extremal black holes, providing a robust theoretical framework for future studies.