One-Loop Corrections to Holographic Shear-Viscosity Ratio Reveal Low-Temperature Violations in Near-Extremal Black Holes

The behaviour of matter at extreme conditions, such as those found near black holes, presents a fundamental challenge to theoretical physics, and understanding the relationship between viscosity and entropy density is crucial to this endeavour. Leopoldo A. Pando Zayas and Jingchao Zhang, both from the University of Michigan, investigate these conditions by exploring quantum fluctuations around near-extremal black holes using the framework of the AdS/CFT correspondence. Their work reveals that these fluctuations generate significant corrections at the quantum level, altering the expected relationship between shear viscosity and entropy density at low temperatures. This discovery challenges established theoretical bounds and provides new insights into the complex interplay between gravity, quantum mechanics, and the thermal properties of matter in these exotic environments.

Quantum fluctuations induce corrections within the gravitational path integral, which are crucial for comprehending the thermodynamics of near-extremal black holes at low temperatures where they surpass the significance of the semi-classical approximation. This research explores the implications of these quantum fluctuations for near-extremal asymptotically AdS4 black branes, specifically within the framework of the AdS/CFT correspondence.

Quantum Corrections to Black Hole Thermodynamics

This paper investigates quantum corrections to the thermodynamics of near-extremal black holes, focusing on how these corrections impact statistical mechanics and potentially resolve issues related to information loss. It builds upon the idea that these black holes exhibit a complex structure that can be explored using techniques from quantum gravity and string theory. A central goal is to understand how quantum effects modify the classical picture of black hole entropy and temperature, and to explore the implications for the holographic principle and the fluid/gravity correspondence. Near-extremal black holes, those close to having zero temperature, are particularly interesting because they exhibit a large entropy and are thought to be sensitive to quantum effects.

The research explores the statistical mechanics of these black holes, relating entropy to the number of microstates, and utilizes the holographic principle, which suggests a connection between gravity and theories without gravity. The fluid/gravity correspondence, a specific realization of the holographic principle, is also employed, where a fluid in a certain spacetime is dual to a gravitational theory in a higher-dimensional spacetime. The study incorporates quantum corrections, modifications to classical physics due to quantum effects, calculated using techniques from string theory and quantum gravity. Researchers considered Schwarzschild and Reissner-Nordström black holes, the simplest types with and without electric charge, and investigated logarithmic corrections, specific quantum corrections appearing in black hole entropy, thought to be related to counting microstates.

The Virasoro algebra and the Heun equation were also key components of the analysis. The paper calculates one-loop quantum corrections to the thermodynamics of near-extremal black holes, finding them to be logarithmic, meaning they modify the entropy in a way that depends on the logarithm of the black hole’s area. These corrections are found to be universal, independent of the specific details of the black hole’s geometry, suggesting they are a fundamental property of quantum gravity. The quantum corrections refine the statistical mechanical description of near-extremal black holes, leading to a more accurate counting of microstates and a better understanding of the black hole’s entropy.

The authors argue that these corrections may help resolve the information paradox, suggesting information may not be completely lost, but encoded in the quantum state of the black hole. A connection is established between the quantum corrections and the Virasoro algebra, suggesting the dynamics of the boundary of a black hole may be described by a conformal field theory. The Heun equation is used to study black hole perturbation theory, providing insights into the black hole’s dynamics and stability.

Schwarzian Fluctuations Correct Near-Extremal Black Hole Gravity

Scientists have achieved a detailed understanding of quantum corrections to the behavior of near-extremal black holes, revealing a breakdown of the semi-classical approximation at low temperatures. The research focuses on fluctuations within the near-horizon region of these black holes, governed by what are known as Schwarzian modes, and their impact on gravitational interactions. Calculations demonstrate that these fluctuations introduce one-loop corrections to the gravitational path integral, becoming increasingly significant as temperatures decrease. The team calculated the influence of these fluctuations on asymptotically AdS black branes using the AdS/CFT correspondence, discovering a coupling between shear gravitational fluctuations and zero modes.

This coupling affects the retarded Green’s function, leading to a violation of the shear viscosity to entropy density bound at low temperatures. Specifically, calculations show that at tree level, the ratio of shear viscosity to entropy density remains constant at 1/4π, even at small temperatures. However, the introduction of one-loop corrections alters this relationship. Measurements reveal that the one-loop correction to the shear viscosity becomes comparable to the linear part of the tree-level result at a characteristic temperature scale. This temperature is found to be much larger than a previously established temperature scale, indicating that quantum effects become prominent earlier than predicted.

The team determined the one-loop correction to the shear viscosity, finding it to grow as temperature decreases. Further analysis shows that the corrected shear viscosity to entropy density ratio deviates from the expected value due to the one-loop contribution. These findings demonstrate a breakdown of the semi-classical approximation at low temperatures and highlight the importance of quantum corrections in understanding the behavior of near-extremal black holes.

Schwarzian Coupling Modifies Black Hole Viscosity

This research investigates the behaviour of near-extremal black holes using the AdS/CFT correspondence, a framework connecting gravity and quantum field theory. The team explored how quantum fluctuations within the black hole’s near-horizon region affect calculations of physical properties on its boundary. Specifically, they examined the gravitational path integral, incorporating one-loop corrections arising from fluctuations to understand their impact on thermodynamic quantities. The key finding demonstrates a coupling between gravitational fluctuations and a specific Schwarzian mode, a type of quantum excitation. This coupling leads to a correction in the calculation of the shear viscosity to entropy density ratio at low temperatures.