[Paper Review] New insights on near-extremal black holes

Gustavo J. Turiaci|arXiv (Cornell University)|Jul 19, 2023

Black Holes and Theoretical PhysicsPhysics and Astronomy3 citations

TL;DR

This paper resolves two puzzles in near-extremal black hole thermodynamics by showing that quantum corrections become arbitrarily large at low temperatures, invalidating the semiclassical description near extremality. Using Jackiw-Teitelboim (JT) gravity, it demonstrates that extremal black holes only exist when protected by low-energy supersymmetry, with a gap in the spectrum ensuring stable ground state degeneracy, while non-supersymmetric extremal black holes are unphysical due to breakdown of classical gravity.

ABSTRACT

We describe two puzzles that arise from a semiclassical treatment of near-extremal black hole thermodynamics. Both puzzles are resolved by realizing that quantum corrections become arbitrarily large at low temperatures, and we explain how the spectrum and dynamics of near-extremal black holes are modified. This analysis also implies that without low energy supersymmetry, such as in the real world, extremal black holes at exactly zero temperature do not exist since the classical picture breaks down completely. In the context of supergravity the analysis is modified; supersymmetric extremal black holes do exist and they are separated from the non-extremal spectrum by a gap power-law suppressed in the entropy. This justifies black hole microstate counting performed in the 90's using string theory.

Motivation & Objective

• To resolve inconsistencies in semiclassical near-extremal black hole thermodynamics arising from divergent quantum corrections at low temperatures.
• To clarify the quantum mechanical nature of extremal black holes, particularly whether they can exist without low-energy supersymmetry.
• To explain why the standard Bekenstein-Hawking entropy formula fails at extremality and how the spectrum is modified by non-perturbative quantum effects.
• To establish the role of JT gravity and its supersymmetric extension (JT supergravity) in deriving a consistent quantum spectrum for near-extremal black holes.
• To justify microstate counting in string theory by showing that a gap in the spectrum stabilizes the ground state degeneracy in supersymmetric extremal black holes.

Proposed method

• The analysis employs the gravitational path integral formalism in Jackiw-Teitelboim (JT) gravity, a solvable model of 2D quantum gravity that captures key features of near-extremal black holes.
• The JT model is extended to JT supergravity to include fermionic modes, which generate a quantum gap in the spectrum when supersymmetry is preserved.
• The spectrum is derived using the Schwarzian theory as the effective description of the conformal symmetry breaking near extremality, with the effective action governing the low-energy dynamics.
• Non-perturbative corrections to the density of states are computed using the effective action, showing exponential growth at high energy and vanishing density at extremality.
• The breakdown scale $ E_{\text{breakdown}} $ is identified as the energy where quantum corrections become strong, signaling the failure of the semiclassical approximation.
• The method compares results with known string theory microstate counts, particularly in the large charge limit, and confirms agreement with logarithmic corrections and gap suppression.

Experimental results

Research questions

• RQ1 Why do standard semiclassical treatments of near-extremal black holes fail at low temperatures, and what replaces them?
• RQ2 Can extremal black holes exist without low-energy supersymmetry, and if not, why?
• RQ3 How do quantum corrections modify the density of states and spectrum of near-extremal black holes?
• RQ4 What is the role of JT gravity and its supersymmetric extension in resolving the quantum structure of extremal black holes?
• RQ5 How does the presence of a gap in the spectrum stabilize the ground state degeneracy in supersymmetric extremal black holes?

Key findings

• Quantum corrections become arbitrarily large at low temperatures, invalidating the semiclassical description of near-extremal black holes and causing the classical picture to break down completely.
• Extremal black holes do not exist in the absence of low-energy supersymmetry, as the semiclassical framework fails at zero temperature due to non-perturbative quantum effects.
• In JT supergravity, a gap $ E_{\text{gap}} = \frac{1}{8} E_{\text{breakdown}}(J=0) = \frac{c^4 \hbar^2}{8 G_N^{1/2} |Q|^3} $ is generated, stabilizing the ground state degeneracy.
• The ground state entropy of supersymmetric extremal black holes is $ \frac{S(T)}{k_B} \approx \frac{\pi Q^2}{c \hbar} + c_{\text{log}} \log\left(\frac{\pi Q^2}{c \hbar}\right) + O(e^{-E_{\text{gap}}/k_B T}) $, with exponentially suppressed thermal corrections.
• The non-perturbative density of states vanishes at extremality, indicating that the classical Bekenstein-Hawking formula fails at zero temperature.
• The results confirm the validity of string theory microstate counting in the 1990s, as the gap and logarithmic corrections match known results from Sen and others.